diff --git a/RELEASES.md b/RELEASES.md
index abb8f04c8..4731d4450 100644
--- a/RELEASES.md
+++ b/RELEASES.md
@@ -15,6 +15,7 @@
 
 #### Closed issues
 
+- Fix `ot.dist` ignoring the weights `w` for the `sqeuclidean`, `euclidean`, `cosine` and `correlation` metrics and for the other metrics computed with `scipy.spatial.distance.cdist` (PR #884)
 - Allow `NumpyBackend.seed` to adopt an existing `np.random.RandomState` instance and remove NumPy-specific random sampling paths in sliced utilities (PR #849, Issue #848)
 - Remove a leftover debug `print` from `ot.utils.projection_sparse_simplex` with `axis=1`, and make the `ot.datasets.make_gauss_hd` docstring a raw string so importing `ot` no longer emits a `SyntaxWarning` (PR #860)
 - Fix the value reported by the entropic unbalanced OT solvers (`ot.unbalanced.sinkhorn_unbalanced`, `sinkhorn_unbalanced2`, `sinkhorn_knopp_unbalanced`, `sinkhorn_stabilized_unbalanced` and `sinkhorn_unbalanced_translation_invariant`, also exposed as `ot.solve(..., reg=..., unbalanced=...).value`): every penalization is now evaluated with the generalized KL divergence, and with `reg_type="entropy"` the constant `dim_a * dim_b` is removed so that the reported value matches the documented negative entropy regularizer. The transport plans are unchanged. `reg_type` is now handled case insensitively by all the methods and an unknown value raises a `ValueError` instead of silently falling back to `"kl"`. The docstrings now state the generalized KL convention, the regularizer `Omega_reg_type(gamma, c)` with its two cases, the keys of the `log` dictionary and the multi-histogram behaviour (PR #874)
diff --git a/ot/utils.py b/ot/utils.py
index 8a40515b1..e2b97feab 100644
--- a/ot/utils.py
+++ b/ot/utils.py
@@ -505,10 +505,13 @@ def dist(
         if w is not None:
             return nx.from_numpy(cdist(x1, x2, metric=metric, w=w))
         return nx.from_numpy(cdist(x1, x2, metric=metric))
-    elif metric == "sqeuclidean":
-        return euclidean_distances(x1, x2, squared=True, nx=nx)
-    elif metric == "euclidean":
-        return euclidean_distances(x1, x2, squared=False, nx=nx)
+    elif metric in ("sqeuclidean", "euclidean"):
+        if w is not None:
+            # sum_k w_k (x1_k - x2_k)^2 is the squared distance between the
+            # samples scaled by sqrt(w)
+            x1 = x1 * nx.sqrt(w)[None, :]
+            x2 = x2 * nx.sqrt(w)[None, :]
+        return euclidean_distances(x1, x2, squared=metric == "sqeuclidean", nx=nx)
     elif metric == "cityblock":
         if w is None:
             if use_tensor:
@@ -557,13 +560,17 @@ def dist(
                 for i in range(x1.shape[1]):
                     M += w[i] * nx.abs(x1[:, i][:, None] - x2[:, i][None, :]) ** p
                 return M ** (1 / p)
-    elif metric == "cosine":
-        nx1 = nx.sqrt(nx.einsum("ij,ij->i", x1, x1))
-        nx2 = nx.sqrt(nx.einsum("ij,ij->i", x2, x2))
-        return 1.0 - (nx.dot(x1, nx.transpose(x2)) / nx1[:, None] / nx2[None, :])
-    elif metric == "correlation":
-        x1 = x1 - nx.mean(x1, axis=1)[:, None]
-        x2 = x2 - nx.mean(x2, axis=1)[:, None]
+    elif metric in ("cosine", "correlation"):
+        if metric == "correlation":
+            if w is None:
+                x1 = x1 - nx.mean(x1, axis=1)[:, None]
+                x2 = x2 - nx.mean(x2, axis=1)[:, None]
+            else:
+                x1 = x1 - (nx.dot(x1, w) / nx.sum(w))[:, None]
+                x2 = x2 - (nx.dot(x2, w) / nx.sum(w))[:, None]
+        if w is not None:
+            x1 = x1 * nx.sqrt(w)[None, :]
+            x2 = x2 * nx.sqrt(w)[None, :]
         nx1 = nx.sqrt(nx.einsum("ij,ij->i", x1, x1))
         nx2 = nx.sqrt(nx.einsum("ij,ij->i", x2, x2))
         return 1.0 - (nx.dot(x1, nx.transpose(x2)) / nx1[:, None] / nx2[None, :])
@@ -573,9 +580,7 @@ def dist(
         else:
             if isinstance(metric, str) and metric.endswith("minkowski"):
                 return cdist(x1, x2, metric=metric, p=p, w=w)
-            # Only pass w parameter for metrics that support it
-            # According to SciPy docs, only 'minkowski' and 'wminkowski' support w
-            if w is not None and metric in ["minkowski", "wminkowski"]:
+            if w is not None:
                 return cdist(x1, x2, metric=metric, w=w)
             return cdist(x1, x2, metric=metric)
 
diff --git a/test/test_utils.py b/test/test_utils.py
index 9c93d520a..986954929 100644
--- a/test/test_utils.py
+++ b/test/test_utils.py
@@ -320,6 +320,45 @@ def test_dist_weighted_cityblock(use_tensor):
     np.testing.assert_allclose(D, expected, atol=1e-12)
 
 
+@pytest.mark.parametrize(
+    "metric",
+    [
+        "sqeuclidean",
+        "euclidean",
+        "cosine",
+        "correlation",
+        "braycurtis",
+        "canberra",
+    ],
+)
+def test_dist_weighted_vs_cdist(metric):
+    rng = np.random.RandomState(0)
+    x1 = rng.randn(5, 3)
+    x2 = rng.randn(4, 3)
+    w = rng.rand(3)
+
+    expected = scipy.spatial.distance.cdist(x1, x2, metric=metric, w=w)
+    D = ot.dist(x1, x2, metric=metric, w=w)
+
+    np.testing.assert_allclose(D, expected, atol=1e-12)
+
+
+@pytest.mark.parametrize(
+    "metric", ["sqeuclidean", "euclidean", "cosine", "correlation"]
+)
+def test_dist_weighted_backends(nx, metric):
+    rng = np.random.RandomState(0)
+    x1 = rng.randn(5, 3)
+    x2 = rng.randn(4, 3)
+    w = rng.rand(3)
+
+    expected = scipy.spatial.distance.cdist(x1, x2, metric=metric, w=w)
+    D = ot.dist(nx.from_numpy(x1), nx.from_numpy(x2), metric=metric, w=nx.from_numpy(w))
+
+    # low atol because jax forces float32
+    np.testing.assert_allclose(nx.to_numpy(D), expected, atol=1e-5)
+
+
 def test_sparse_ot_dist_uses_pair_weights():
     x1 = np.array([[0.0], [1.0]])
     x2 = np.array([[0.0], [5.0]])