diff --git a/lib/matplotlib/font_manager.py b/lib/matplotlib/font_manager.py
index 3e9a164d1458..4d77e1da373c 100644
--- a/lib/matplotlib/font_manager.py
+++ b/lib/matplotlib/font_manager.py
@@ -346,6 +346,7 @@ def findSystemFonts(fontpaths=None, fontext='ttf'):
     return [fname for fname in fontfiles if os.path.exists(fname)]
 
 
+@cbook.deprecated("2.1")
 def weight_as_number(weight):
     """
     Return the weight property as a numeric value.  String values
@@ -435,17 +436,12 @@ def ttfFontProperty(font):
     else:
         variant = 'normal'
 
-    #  Weights are: 100, 200, 300, 400 (normal: default), 500 (medium),
-    #    600 (semibold, demibold), 700 (bold), 800 (heavy), 900 (black)
-    #    lighter and bolder are also allowed.
-
     weight = next((w for w in weight_dict if sfnt4.find(w) >= 0), None)
     if not weight:
         if font.style_flags & ft2font.BOLD:
             weight = 700
         else:
             weight = 400
-    weight = weight_as_number(weight)
 
     #  Stretch can be absolute and relative
     #  Absolute stretches are: ultra-condensed, extra-condensed, condensed,
@@ -511,11 +507,7 @@ def afmFontProperty(fontpath, font):
     else:
         variant = 'normal'
 
-    #  Weights are: 100, 200, 300, 400 (normal: default), 500 (medium),
-    #    600 (semibold, demibold), 700 (bold), 800 (heavy), 900 (black)
-    #    lighter and bolder are also allowed.
-
-    weight = weight_as_number(font.get_weight().lower())
+    weight = font.get_weight().lower()
 
     #  Stretch can be absolute and relative
     #  Absolute stretches are: ultra-condensed, extra-condensed, condensed,
@@ -855,7 +847,6 @@ def set_weight(self, weight):
         except ValueError:
             if weight not in weight_dict:
                 raise ValueError("weight is invalid")
-            weight = weight_dict[weight]
         self._weight = weight
 
     def set_stretch(self, stretch):
@@ -1203,10 +1194,19 @@ def score_weight(self, weight1, weight2):
         """
         Returns a match score between *weight1* and *weight2*.
 
-        The result is the absolute value of the difference between the
+        The result is 0.0 if both weight1 and weight 2 are given as strings
+        and have the same value.
+
+        Otherwise, the result is the absolute value of the difference between the
         CSS numeric values of *weight1* and *weight2*, normalized
-        between 0.0 and 1.0.
+        between 0.05 and 1.0.
         """
+
+        # exact match of the weight names (e.g. weight1 == weight2 == "regular")
+        if (isinstance(weight1, six.string_types) and
+                isinstance(weight2, six.string_types) and
+                weight1 == weight2):
+            return 0.0
         try:
             weightval1 = int(weight1)
         except ValueError:
@@ -1215,7 +1215,7 @@ def score_weight(self, weight1, weight2):
             weightval2 = int(weight2)
         except ValueError:
             weightval2 = weight_dict.get(weight2, 500)
-        return abs(weightval1 - weightval2) / 1000.0
+        return 0.95*(abs(weightval1 - weightval2) / 1000.0) + 0.05
 
     def score_size(self, size1, size2):
         """
diff --git a/lib/matplotlib/tests/test_font_manager.py b/lib/matplotlib/tests/test_font_manager.py
index 90785e8f4985..8adf601322fc 100644
--- a/lib/matplotlib/tests/test_font_manager.py
+++ b/lib/matplotlib/tests/test_font_manager.py
@@ -31,6 +31,17 @@ def test_font_priority():
     assert cmap[8729] == 30
 
 
+def test_score_weight():
+    assert 0 == fontManager.score_weight("regular", "regular")
+    assert 0 == fontManager.score_weight("bold", "bold")
+    assert (0 < fontManager.score_weight(400, 400) <
+            fontManager.score_weight("normal", "bold"))
+    assert (0 < fontManager.score_weight("normal", "regular") <
+            fontManager.score_weight("normal", "bold"))
+    assert (fontManager.score_weight("normal", "regular") ==
+            fontManager.score_weight(400, 400))
+
+
 def test_json_serialization():
     # on windows, we can't open a file twice, so save the name and unlink
     # manually...