diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 990962673b8..5c0d3c3c843 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -42,6 +42,8 @@ Performance
 
 Bug fixes
 ~~~~~~~~~
+- Fix bug where weighted ``polyfit`` were changing the original object (:issue:`5644`, :pull:`7900`).
+  By `Mattia Almansi <https://github.com/malmans2>`_.
 - Don't call ``CachingFileManager.__del__`` on interpreter shutdown (:issue:`7814`, :pull:`7880`).
   By `Justus Magin <https://github.com/keewis>`_.
 
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 81860bede95..0f271e9d7e4 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -7972,7 +7972,7 @@ def polyfit(
                 scale_da = scale
 
             if w is not None:
-                rhs *= w[:, np.newaxis]
+                rhs = rhs * w[:, np.newaxis]
 
             with warnings.catch_warnings():
                 if full:  # Copy np.polyfit behavior
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index cc9220dfe33..01c26ad6104 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -6217,6 +6217,14 @@ def test_polyfit_output(self) -> None:
         out = ds.polyfit("time", 2)
         assert len(out.data_vars) == 0
 
+    def test_polyfit_weighted(self) -> None:
+        # Make sure weighted polyfit does not change the original object (issue #5644)
+        ds = create_test_data(seed=1)
+        ds_copy = ds.copy(deep=True)
+
+        ds.polyfit("dim2", 2, w=np.arange(ds.sizes["dim2"]))
+        xr.testing.assert_identical(ds, ds_copy)
+
     def test_polyfit_warnings(self) -> None:
         ds = create_test_data(seed=1)