Flour weights

For all the experts on this list, Please give us your recommendations on
 how much one cup of flour should weigh for bread baking!
 
 I know that by weighing flour, as opposed to measuring it, that I can
 achieve more consistent results in my bread machine. It is also easier to
 weigh flour than it is to "sprinkle" the flour into a cup.
 
 My dilemna is that I have seen widely varying weights for one cup of flour.
 I also know that all flours do not weigh the same, ie, one cup of bread
 flour does not weigh the same as one cup of rye.
 
  Weight of flour PER CUP:
 
 4 3/8   ounces  or 125  grams   all-purpose flour   (USDA)
 4 5/8   ounces  or 130  grams   all-purpose flour   (Gold Medal)
 
 4 1/4   ounces  or  120 grams   whole wheat flour  (USDA)
 4 1/2   ounces  or  128 grams   whole wheat flour  (Gold Medal)
 
 4 1/2   ounces  or  127 grams   bread flour     (USDA)
 4 3/4   ounces  or  135 grams   bread flour     (Gold Medal)
 
 3 5/8   ounces  or  102 grams   rye flour       (USDA)
 
 King Arthur says ALL flour types weigh 4 oz (113 grams) per cup.
 
 This variance ranges from as little as one tablespoon up to 8 tablespoons
 per cup of flour! Now, that is a lot of difference!
 
 In my own weighing, I have found that one cup of flour for me is usually
 within the range of the USDA and Gold Medal numbers, but I can make a cup
 weigh almost anything I want. :-)
 
 I cannot believe the King Arthur number of only 4 ounces per cup of flour.
 I am finding that I typically need to reduce the water in my bread by 1-2
 tablespoons using the heavier cups of flour. If I used the KA 4 oz., I'd
 have mud, not dough. And, in the case of a rye loaf, it would be much too
 dry.