diff --git a/stdlib/@tests/stubtest_allowlists/common.txt b/stdlib/@tests/stubtest_allowlists/common.txt
index 784599491..cba2f2149 100644
--- a/stdlib/@tests/stubtest_allowlists/common.txt
+++ b/stdlib/@tests/stubtest_allowlists/common.txt
@@ -540,7 +540,6 @@ wsgiref.handlers.BaseHandler.result
 wsgiref.handlers.BaseHandler.status
 
 (_?weakref.ref|_?weakref.ReferenceType).__call__  # C function default annotation is wrong
-(_?weakref.ref|_?weakref.ReferenceType).__init__  # Runtime defines __new__ but stubtest thinks __init__ is also defined.
 _?weakref.CallableProxyType.__getattr__  # Should have all attributes of proxy
 _?weakref.ProxyType.__bytes__  # Doesn't actually exist
 _?weakref.ProxyType.__getattr__  # Should have all attributes of proxy
diff --git a/stdlib/_weakref.pyi b/stdlib/_weakref.pyi
index 61365645d..f142820c5 100644
--- a/stdlib/_weakref.pyi
+++ b/stdlib/_weakref.pyi
@@ -21,8 +21,9 @@ class ProxyType(Generic[_T]):  # "weakproxy"
     def __getattr__(self, attr: str) -> Any: ...
 
 class ReferenceType(Generic[_T]):
-    __callback__: Callable[[ReferenceType[_T]], Any]
-    def __new__(cls, o: _T, callback: Callable[[ReferenceType[_T]], Any] | None = ..., /) -> Self: ...
+    __callback__: Callable[[Self], Any]
+    def __new__(cls, o: _T, callback: Callable[[Self], Any] | None = ..., /) -> Self: ...
+    def __init__(self, o: _T, callback: Callable[[Self], Any] | None = ..., /) -> None: ...
     def __call__(self) -> _T | None: ...
     def __eq__(self, value: object, /) -> bool: ...
     def __hash__(self) -> int: ...
diff --git a/stdlib/weakref.pyi b/stdlib/weakref.pyi
index e34512423..aaba7ffc9 100644
--- a/stdlib/weakref.pyi
+++ b/stdlib/weakref.pyi
@@ -41,7 +41,10 @@ _P = ParamSpec("_P")
 ProxyTypes: tuple[type[Any], ...]
 
 class WeakMethod(ref[_CallableT]):
-    def __new__(cls, meth: _CallableT, callback: Callable[[Self], object] | None = None) -> Self: ...
+    # `ref` is implemented in `C` so positional-only arguments are enforced, but not in `WeakMethod`.
+    def __new__(  # pyright: ignore[reportInconsistentConstructor]
+        cls, meth: _CallableT, callback: Callable[[Self], Any] | None = None
+    ) -> Self: ...
     def __call__(self) -> _CallableT | None: ...
     def __eq__(self, other: object) -> bool: ...
     def __ne__(self, other: object) -> bool: ...