diff --git a/stubs/seaborn/@tests/stubtest_allowlist.txt b/stubs/seaborn/@tests/stubtest_allowlist.txt
index 9265bb405..d2456463b 100644
--- a/stubs/seaborn/@tests/stubtest_allowlist.txt
+++ b/stubs/seaborn/@tests/stubtest_allowlist.txt
@@ -2,6 +2,4 @@ seaborn._core.scales.(Pipeline|TransFuncs)  # aliases defined in `if TYPE_CHECKI
 seaborn.external.docscrape.ClassDoc.__init__  # stubtest doesn't like ABC class as default value
 seaborn.external.docscrape.NumpyDocString.__str__  # weird signature
 
-seaborn(\.regression)?\.lmplot  # the `data` argument is required but it defaults to `None` at runtime
-
 seaborn.axisgrid.Grid.tight_layout  # the method doesn't really take pos args but runtime has *args
diff --git a/stubs/seaborn/METADATA.toml b/stubs/seaborn/METADATA.toml
index c8c7b7880..d8378c374 100644
--- a/stubs/seaborn/METADATA.toml
+++ b/stubs/seaborn/METADATA.toml
@@ -1,4 +1,4 @@
-version = "0.13.0"
+version = "0.13.1"
 # Requires a version of numpy and matplotlib with a `py.typed` file
 requires = ["matplotlib>=3.8", "numpy>=1.20", "pandas-stubs"]
 # matplotlib>=3.8 requires Python >=3.9
diff --git a/stubs/seaborn/seaborn/_core/plot.pyi b/stubs/seaborn/seaborn/_core/plot.pyi
index 937814221..cfe70fc10 100644
--- a/stubs/seaborn/seaborn/_core/plot.pyi
+++ b/stubs/seaborn/seaborn/_core/plot.pyi
@@ -98,8 +98,14 @@ class Plot:
     def share(self, **shares: bool | str) -> Plot: ...
     def limit(self, **limits: tuple[Any, Any]) -> Plot: ...
     def label(self, *, title: str | None = None, legend: str | None = None, **variables: str | Callable[[str], str]) -> Plot: ...
-    def layout(self, *, size: tuple[float, float] | Default = ..., engine: str | None | Default = ...) -> Plot: ...
-    def theme(self, *args: dict[str, Any]) -> Plot: ...
+    def layout(
+        self,
+        *,
+        size: tuple[float, float] | Default = ...,
+        engine: str | None | Default = ...,
+        extent: tuple[float, float, float, float] | Default = ...,
+    ) -> Plot: ...
+    def theme(self, __config: dict[str, Any]) -> Plot: ...
     # Same signature as Plotter.save
     def save(
         self,
diff --git a/stubs/seaborn/seaborn/_core/typing.pyi b/stubs/seaborn/seaborn/_core/typing.pyi
index 35aa0f4fe..25f823c8e 100644
--- a/stubs/seaborn/seaborn/_core/typing.pyi
+++ b/stubs/seaborn/seaborn/_core/typing.pyi
@@ -1,14 +1,15 @@
 from _typeshed import Incomplete
 from collections.abc import Iterable, Mapping
 from datetime import date, datetime, timedelta
-from typing import Any, Protocol
+from typing import Any, Protocol, type_check_only
 from typing_extensions import TypeAlias
 
 from matplotlib.colors import Colormap, Normalize
 from numpy import ndarray
 from pandas import DataFrame, Index, Series, Timedelta, Timestamp
 
-class _SupportsDataFrame(Protocol):
+@type_check_only
+class SupportsDataFrame(Protocol):
     # `__dataframe__` should return pandas.core.interchange.dataframe_protocol.DataFrame
     # but this class needs to be defined as a Protocol, not as an ABC.
     def __dataframe__(self, nan_as_null: bool = ..., allow_copy: bool = ...) -> Incomplete: ...
@@ -17,7 +18,7 @@ ColumnName: TypeAlias = str | bytes | date | datetime | timedelta | bool | compl
 Vector: TypeAlias = Series[Any] | Index[Any] | ndarray[Any, Any]
 VariableSpec: TypeAlias = ColumnName | Vector | None
 VariableSpecList: TypeAlias = list[VariableSpec] | Index[Any] | None
-DataSource: TypeAlias = DataFrame | _SupportsDataFrame | Mapping[ColumnName, Incomplete] | None
+DataSource: TypeAlias = DataFrame | SupportsDataFrame | Mapping[Any, Incomplete] | None
 OrderSpec: TypeAlias = Iterable[str] | None
 NormSpec: TypeAlias = tuple[float | None, float | None] | Normalize | None
 PaletteSpec: TypeAlias = str | list[Incomplete] | dict[Incomplete, Incomplete] | Colormap | None
diff --git a/stubs/seaborn/seaborn/axisgrid.pyi b/stubs/seaborn/seaborn/axisgrid.pyi
index fb80ef7f7..760415d75 100644
--- a/stubs/seaborn/seaborn/axisgrid.pyi
+++ b/stubs/seaborn/seaborn/axisgrid.pyi
@@ -8,7 +8,7 @@ import numpy as np
 from matplotlib.artist import Artist
 from matplotlib.axes import Axes
 from matplotlib.backend_bases import MouseEvent, RendererBase
-from matplotlib.colors import Colormap, Normalize
+from matplotlib.colors import Colormap
 from matplotlib.figure import Figure
 from matplotlib.font_manager import FontProperties
 from matplotlib.gridspec import SubplotSpec
@@ -23,7 +23,7 @@ from matplotlib.typing import ColorType, LineStyleType, MarkerType
 from numpy.typing import ArrayLike, NDArray
 from pandas import DataFrame, Series
 
-from ._core.typing import ColumnName, DataSource, _SupportsDataFrame
+from ._core.typing import ColumnName, DataSource, NormSpec, SupportsDataFrame
 from .palettes import _RGBColorPalette
 from .utils import _DataSourceWideForm, _Palette, _Vector
 
@@ -155,7 +155,7 @@ class Grid(_BaseGrid):
         ncols: int = 1,
         mode: Literal["expand"] | None = None,
         fancybox: bool | None = None,
-        shadow: bool | dict[str, float] | None = None,
+        shadow: bool | dict[str, int] | dict[str, float] | None = None,
         title_fontsize: int | _LiteralFont | None = None,
         framealpha: float | None = None,
         edgecolor: ColorType | None = None,
@@ -212,7 +212,7 @@ class FacetGrid(Grid):
     hue_kws: dict[str, Any]
     def __init__(
         self,
-        data: DataFrame | _SupportsDataFrame,
+        data: DataFrame | SupportsDataFrame,
         *,
         row: str | None = None,
         col: str | None = None,
@@ -293,7 +293,7 @@ class PairGrid(Grid):
     palette: _RGBColorPalette
     def __init__(
         self,
-        data: DataFrame | _SupportsDataFrame,
+        data: DataFrame | SupportsDataFrame,
         *,
         hue: str | None = None,
         vars: Iterable[str] | None = None,
@@ -335,7 +335,7 @@ class JointGrid(_BaseGrid):
         space: float = 0.2,
         palette: _Palette | Colormap | None = None,
         hue_order: Iterable[ColumnName] | None = None,
-        hue_norm: tuple[float, float] | Normalize | None = None,
+        hue_norm: NormSpec = None,
         dropna: bool = False,
         xlim: float | tuple[float, float] | None = None,
         ylim: float | tuple[float, float] | None = None,
@@ -394,7 +394,7 @@ def jointplot(
     color: ColorType | None = None,
     palette: _Palette | Colormap | None = None,
     hue_order: Iterable[ColumnName] | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     marginal_ticks: bool = False,
     joint_kws: dict[str, Any] | None = None,
     marginal_kws: dict[str, Any] | None = None,
diff --git a/stubs/seaborn/seaborn/categorical.pyi b/stubs/seaborn/seaborn/categorical.pyi
index 806ab5b57..88bef485b 100644
--- a/stubs/seaborn/seaborn/categorical.pyi
+++ b/stubs/seaborn/seaborn/categorical.pyi
@@ -3,10 +3,9 @@ from collections.abc import Callable, Iterable
 from typing import Any, Literal
 
 from matplotlib.axes import Axes
-from matplotlib.colors import Normalize
 from matplotlib.typing import ColorType, LineStyleType, MarkerType
 
-from ._core.typing import ColumnName, DataSource, Default
+from ._core.typing import ColumnName, DataSource, Default, NormSpec
 from .axisgrid import FacetGrid
 from .external.kde import _BwMethodType
 from .utils import _DataSourceWideForm, _ErrorBar, _Estimator, _Legend, _LogScale, _Palette, _Seed, _Vector
@@ -33,7 +32,7 @@ def boxplot(
     linecolor: ColorType = "auto",
     linewidth: float | None = None,
     fliersize: float | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     native_scale: bool = False,
     log_scale: _LogScale | None = None,
     formatter: Callable[[Any], str] | None = None,
@@ -67,7 +66,7 @@ def violinplot(
     bw_adjust: float = 1,
     density_norm: Literal["area", "count", "width"] = "area",
     common_norm: bool | None = False,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     formatter: Callable[[Any], str] | None = None,
     log_scale: _LogScale | None = None,
     native_scale: bool = False,
@@ -102,7 +101,7 @@ def boxenplot(
     outlier_prop: float = 0.007,
     trust_alpha: float = 0.05,
     showfliers: bool = True,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     log_scale: _LogScale | None = None,
     native_scale: bool = False,
     formatter: Callable[[Any], str] | None = None,
@@ -130,7 +129,7 @@ def stripplot(
     size: float = 5,
     edgecolor: ColorType | Default = ...,
     linewidth: float = 0,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     log_scale: _LogScale | None = None,
     native_scale: bool = False,
     formatter: Callable[[Any], str] | None = None,
@@ -153,7 +152,7 @@ def swarmplot(
     size: float = 5,
     edgecolor: ColorType | None = None,
     linewidth: float = 0,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     log_scale: _LogScale | None = None,
     native_scale: bool = False,
     formatter: Callable[[Any], str] | None = None,
@@ -174,13 +173,14 @@ def barplot(
     errorbar: _ErrorBar | None = ("ci", 95),
     n_boot: int = 1000,
     units: ColumnName | _Vector | None = None,
+    weights: ColumnName | _Vector | None = None,
     seed: _Seed | None = None,
     orient: Literal["v", "h", "x", "y"] | None = None,
     color: ColorType | None = None,
     palette: _Palette | None = None,
     saturation: float = 0.75,
     fill: bool = True,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     width: float = 0.8,
     dodge: bool | Literal["auto"] = "auto",
     gap: float = 0,
@@ -208,10 +208,11 @@ def pointplot(
     errorbar: _ErrorBar | None = ("ci", 95),
     n_boot: int = 1000,
     units: ColumnName | _Vector | None = None,
+    weights: ColumnName | _Vector | None = None,
     seed: _Seed | None = None,
     color: ColorType | None = None,
     palette: _Palette | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     markers: MarkerType | list[MarkerType] | Default = ...,
     linestyles: LineStyleType | list[LineStyleType] | Default = ...,
     dodge: bool = False,
@@ -242,7 +243,7 @@ def countplot(
     palette: _Palette | None = None,
     saturation: float = 0.75,
     fill: bool = True,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     stat: Literal["count", "percent", "proportion", "probability"] = "count",
     width: float = 0.8,
     dodge: bool | Literal["auto"] = "auto",
@@ -267,6 +268,7 @@ def catplot(
     errorbar: _ErrorBar | None = ("ci", 95),
     n_boot: int = 1000,
     units: ColumnName | _Vector | None = None,
+    weights: ColumnName | _Vector | None = None,
     seed: _Seed | None = None,
     order: Iterable[ColumnName] | None = None,
     hue_order: Iterable[ColumnName] | None = None,
@@ -281,7 +283,7 @@ def catplot(
     orient: Literal["v", "h", "x", "y"] | None = None,
     color: ColorType | None = None,
     palette: _Palette | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     legend: _Legend = "auto",
     legend_out: bool = True,
     sharex: bool = True,
diff --git a/stubs/seaborn/seaborn/distributions.pyi b/stubs/seaborn/seaborn/distributions.pyi
index e00f4df74..0f426084b 100644
--- a/stubs/seaborn/seaborn/distributions.pyi
+++ b/stubs/seaborn/seaborn/distributions.pyi
@@ -3,11 +3,11 @@ from typing import Any, Literal, Protocol, TypeVar
 from typing_extensions import TypeAlias, deprecated
 
 from matplotlib.axes import Axes
-from matplotlib.colors import Colormap, Normalize
+from matplotlib.colors import Colormap
 from matplotlib.typing import ColorType
 from numpy.typing import ArrayLike
 
-from ._core.typing import ColumnName, DataSource
+from ._core.typing import ColumnName, DataSource, NormSpec
 from .axisgrid import FacetGrid
 from .external.kde import _BwMethodType
 from .utils import _DataSourceWideForm, _LogScale, _Palette, _Vector
@@ -51,7 +51,7 @@ def histplot(
     cbar_kws: dict[str, Any] | None = None,
     palette: _Palette | Colormap | None = None,
     hue_order: Iterable[ColumnName] | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     color: ColorType | None = None,
     log_scale: _LogScale | None = None,
     legend: bool = True,
@@ -67,7 +67,7 @@ def kdeplot(
     weights: ColumnName | _Vector | None = None,
     palette: _Palette | Colormap | None = None,
     hue_order: Iterable[ColumnName] | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     color: ColorType | None = None,
     fill: bool | None = None,
     multiple: Literal["layer", "stack", "fill"] = "layer",
@@ -101,7 +101,7 @@ def ecdfplot(
     complementary: bool = False,
     palette: _Palette | Colormap | None = None,
     hue_order: Iterable[ColumnName] | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     log_scale: _LogScale | None = None,
     legend: bool = True,
     ax: Axes | None = None,
@@ -117,7 +117,7 @@ def rugplot(
     expand_margins: bool = True,
     palette: _Palette | Colormap | None = None,
     hue_order: Iterable[ColumnName] | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     legend: bool = True,
     ax: Axes | None = None,
     **kwargs: Any,
@@ -138,7 +138,7 @@ def displot(
     legend: bool = True,
     palette: _Palette | Colormap | None = None,
     hue_order: Iterable[ColumnName] | None = None,
-    hue_norm: tuple[float, float] | Normalize | None = None,
+    hue_norm: NormSpec = None,
     color: ColorType | None = None,
     col_wrap: int | None = None,
     row_order: Iterable[ColumnName] | None = None,
diff --git a/stubs/seaborn/seaborn/relational.pyi b/stubs/seaborn/seaborn/relational.pyi
index b9278199b..7a7bde159 100644
--- a/stubs/seaborn/seaborn/relational.pyi
+++ b/stubs/seaborn/seaborn/relational.pyi
@@ -1,36 +1,42 @@
-from _typeshed import Incomplete
-from collections.abc import Iterable
+from collections.abc import Iterable, Mapping, Sequence
 from typing import Any, Literal
 from typing_extensions import TypeAlias
 
 from matplotlib.axes import Axes
 from matplotlib.colors import Colormap
+from matplotlib.typing import MarkerType
 
+from ._core.typing import ColumnName, DataSource, NormSpec
 from .axisgrid import FacetGrid
-from .utils import _ErrorBar, _Estimator, _Legend, _Palette, _Seed
+from .utils import _DataSourceWideForm, _ErrorBar, _Estimator, _Legend, _Palette, _Seed, _Vector
 
 __all__ = ["relplot", "scatterplot", "lineplot"]
 
-_Sizes: TypeAlias = list[float] | dict[str, float] | tuple[float, float]
+_Sizes: TypeAlias = list[int] | list[float] | dict[str, int] | dict[str, float] | tuple[float, float]
+_DashType: TypeAlias = tuple[None, None] | Sequence[float]  # See matplotlib.lines.Line2D.set_dashes
+# "dashes" and "markers" require dict but we use mapping to avoid long unions because dict is invariant in its value type
+_Dashes: TypeAlias = bool | Sequence[_DashType] | Mapping[Any, _DashType]
+_Markers: TypeAlias = bool | Sequence[MarkerType] | Mapping[Any, MarkerType]
 
 def lineplot(
-    data: Incomplete | None = None,
+    data: DataSource | _DataSourceWideForm | None = None,
     *,
-    x: Incomplete | None = None,
-    y: Incomplete | None = None,
-    hue: Incomplete | None = None,
-    size: Incomplete | None = None,
-    style: Incomplete | None = None,
-    units: Incomplete | None = None,
+    x: ColumnName | _Vector | None = None,
+    y: ColumnName | _Vector | None = None,
+    hue: ColumnName | _Vector | None = None,
+    size: ColumnName | _Vector | None = None,
+    style: ColumnName | _Vector | None = None,
+    units: ColumnName | _Vector | None = None,
+    weights: ColumnName | _Vector | None = None,
     palette: _Palette | Colormap | None = None,
-    hue_order: Iterable[Any] | None = None,
-    hue_norm: Incomplete | None = None,
+    hue_order: Iterable[ColumnName] | None = None,
+    hue_norm: NormSpec = None,
     sizes: _Sizes | None = None,
-    size_order: Iterable[Any] | None = None,
-    size_norm: Incomplete | None = None,
-    dashes: bool | list[Incomplete] | dict[str, Incomplete] = True,
-    markers: Incomplete | None = None,
-    style_order: Iterable[Any] | None = None,
+    size_order: Iterable[ColumnName] | None = None,
+    size_norm: NormSpec = None,
+    dashes: _Dashes | None = True,
+    markers: _Markers | None = None,
+    style_order: Iterable[ColumnName] | None = None,
     estimator: _Estimator | None = "mean",
     errorbar: _ErrorBar | None = ("ci", 95),
     n_boot: int = 1000,
@@ -45,48 +51,49 @@ def lineplot(
     **kwargs: Any,
 ) -> Axes: ...
 def scatterplot(
-    data: Incomplete | None = None,
+    data: DataSource | _DataSourceWideForm | None = None,
     *,
-    x: Incomplete | None = None,
-    y: Incomplete | None = None,
-    hue: Incomplete | None = None,
-    size: Incomplete | None = None,
-    style: Incomplete | None = None,
+    x: ColumnName | _Vector | None = None,
+    y: ColumnName | _Vector | None = None,
+    hue: ColumnName | _Vector | None = None,
+    size: ColumnName | _Vector | None = None,
+    style: ColumnName | _Vector | None = None,
     palette: _Palette | Colormap | None = None,
-    hue_order: Iterable[Any] | None = None,
-    hue_norm: Incomplete | None = None,
+    hue_order: Iterable[ColumnName] | None = None,
+    hue_norm: NormSpec = None,
     sizes: _Sizes | None = None,
-    size_order: Iterable[Any] | None = None,
-    size_norm: Incomplete | None = None,
-    markers: Incomplete = True,
-    style_order: Iterable[Any] | None = None,
+    size_order: Iterable[ColumnName] | None = None,
+    size_norm: NormSpec = None,
+    markers: _Markers | None = True,
+    style_order: Iterable[ColumnName] | None = None,
     legend: _Legend = "auto",
     ax: Axes | None = None,
     **kwargs: Any,
 ) -> Axes: ...
 def relplot(
-    data: Incomplete | None = None,
+    data: DataSource | _DataSourceWideForm | None = None,
     *,
-    x: Incomplete | None = None,
-    y: Incomplete | None = None,
-    hue: Incomplete | None = None,
-    size: Incomplete | None = None,
-    style: Incomplete | None = None,
-    units: Incomplete | None = None,
-    row: Incomplete | None = None,
-    col: Incomplete | None = None,
+    x: ColumnName | _Vector | None = None,
+    y: ColumnName | _Vector | None = None,
+    hue: ColumnName | _Vector | None = None,
+    size: ColumnName | _Vector | None = None,
+    style: ColumnName | _Vector | None = None,
+    units: ColumnName | _Vector | None = None,
+    weights: ColumnName | _Vector | None = None,
+    row: ColumnName | _Vector | None = None,
+    col: ColumnName | _Vector | None = None,
     col_wrap: int | None = None,
-    row_order: Iterable[Any] | None = None,
-    col_order: Iterable[Any] | None = None,
+    row_order: Iterable[ColumnName] | None = None,
+    col_order: Iterable[ColumnName] | None = None,
     palette: _Palette | Colormap | None = None,
-    hue_order: Iterable[Any] | None = None,
-    hue_norm: Incomplete | None = None,
+    hue_order: Iterable[ColumnName] | None = None,
+    hue_norm: NormSpec = None,
     sizes: _Sizes | None = None,
-    size_order: Iterable[Any] | None = None,
-    size_norm: Incomplete | None = None,
-    markers: Incomplete | None = None,
-    dashes: Incomplete | None = None,
-    style_order: Iterable[Any] | None = None,
+    size_order: Iterable[ColumnName] | None = None,
+    size_norm: NormSpec = None,
+    markers: _Markers | None = None,
+    dashes: _Dashes | None = None,
+    style_order: Iterable[ColumnName] | None = None,
     legend: _Legend = "auto",
     kind: Literal["scatter", "line"] = "scatter",
     height: float = 5,
diff --git a/stubs/seaborn/seaborn/utils.pyi b/stubs/seaborn/seaborn/utils.pyi
index 008e27bbf..ac0abf222 100644
--- a/stubs/seaborn/seaborn/utils.pyi
+++ b/stubs/seaborn/seaborn/utils.pyi
@@ -14,7 +14,8 @@ from matplotlib.ticker import Locator
 from matplotlib.typing import ColorType
 from numpy.typing import ArrayLike, NDArray
 from pandas import DataFrame
-from seaborn.axisgrid import Grid
+
+from .axisgrid import Grid
 
 __all__ = [
     "desaturate",
@@ -34,7 +35,8 @@ _ErrorBar: TypeAlias = str | tuple[str, float] | Callable[[Iterable[float]], tup
 _Estimator: TypeAlias = str | Callable[..., Incomplete]  # noqa: Y047
 _Legend: TypeAlias = Literal["auto", "brief", "full"] | bool  # noqa: Y047
 _LogScale: TypeAlias = bool | float | tuple[bool | float, bool | float]  # noqa: Y047
-_Palette: TypeAlias = str | Sequence[ColorType] | dict[Incomplete, ColorType]  # noqa: Y047
+# `palette` requires dict but we use mapping to avoid a very long union because dict is invariant in its value type
+_Palette: TypeAlias = str | Sequence[ColorType] | Mapping[Any, ColorType]  # noqa: Y047
 _Seed: TypeAlias = int | np.random.Generator | np.random.RandomState  # noqa: Y047
 _Scalar: TypeAlias = (
     # numeric
@@ -60,7 +62,7 @@ _DataSourceWideForm: TypeAlias = (  # noqa: Y047
     # Sequence of "convertible to pd.Series" vectors
     | Sequence[_Vector]
     # A "convertible to pd.DataFrame" table
-    | Mapping[Any, Mapping[_Scalar, _Scalar]]
+    | Mapping[Any, Mapping[Any, _Scalar]]
     | NDArray[Any]
     # Flat "convertible to pd.Series" vector of scalars
     | Sequence[_Scalar]