diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index 552f1d243dcc3..2c27cb5f548c2 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -750,8 +750,10 @@ def check_sample_weights_invariance(name, estimator_orig):
 
         estimator1 = clone(estimator_orig)
         estimator2 = clone(estimator_orig)
+        estimator3 = clone(estimator_orig)
         set_random_state(estimator1, random_state=0)
         set_random_state(estimator2, random_state=0)
+        set_random_state(estimator3, random_state=0)
 
         X = np.array([[1, 3], [1, 3], [1, 3], [1, 3],
                       [2, 1], [2, 1], [2, 1], [2, 1],
@@ -759,22 +761,40 @@ def check_sample_weights_invariance(name, estimator_orig):
                       [4, 1], [4, 1], [4, 1], [4, 1]], dtype=np.dtype('float'))
         y = np.array([1, 1, 1, 1, 2, 2, 2, 2,
                       1, 1, 1, 1, 2, 2, 2, 2], dtype=np.dtype('int'))
+
+        X2 = np.vstack([X, X])
+        y2 = np.hstack([y, 3 - y])
         y = _enforce_estimator_tags_y(estimator1, y)
+        y2 = _enforce_estimator_tags_y(estimator3, y2)
+        weights = np.ones(shape=len(y) * 2)
+        weights[len(y):] = 0
+        X2, y2, weights = shuffle(X2, y2, weights, random_state=0)
 
         estimator1.fit(X, y=y, sample_weight=np.ones(shape=len(y)))
         estimator2.fit(X, y=y, sample_weight=None)
+        estimator3.fit(X2, y=y2, sample_weight=weights)
 
-        for method in ["predict", "transform"]:
+        for method in ["predict", "predict_proba",
+                       "decision_function", "transform"]:
             if hasattr(estimator_orig, method):
                 X_pred1 = getattr(estimator1, method)(X)
                 X_pred2 = getattr(estimator2, method)(X)
+                X_pred3 = getattr(estimator3, method)(X)
                 if sparse.issparse(X_pred1):
                     X_pred1 = X_pred1.toarray()
                     X_pred2 = X_pred2.toarray()
+                    X_pred3 = X_pred3.toarray()
                 assert_allclose(X_pred1, X_pred2,
                                 err_msg="For %s sample_weight=None is not"
                                         " equivalent to sample_weight=ones"
                                         % name)
+                assert_allclose(
+                    X_pred1, X_pred3,
+                    err_msg="For %s sample_weight is not"
+                            " equivalent to removing samples"
+                            % name)
+
+
 
 
 @ignore_warnings(category=(DeprecationWarning, FutureWarning, UserWarning))