This is what King Arthur has to say on the matter.
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Measuring flour
At King Arthur Flour, we’ve held a long debate about what a “cup” of flour weighs. In the past, for simplicity’s sake, we called it 4 ounces. You can, in fact, create a 4-ounce cup of flour by sifting the flour first. The sifting process incorporates a lot of air into the flour, which is the first source of leavening. Scooping flour, which can produce a much heavier cup (up to 5 1/2 ounces plus), will obviously contain less air and more flour. So our old volume measurement for flour, when it meant 4 ounces, had its positive benefits, at least as far as leavening was concerned. You can also fluff flour up in your flour bag, sprinkle it gently into your measuring cup, scrape the top off with a straight edge, and get close to 4 ounces, but you probably will get a little bit more.
Our preferred weight for a cup of flour is 4 1/4 ounces, and that’s what we’ve used throughout the book. This is closer to what bakers actually measure volume-wise. It does make calculating total ounces a little more difficult, but in all of the recipes, we’ve done the calculating for you. This discussion would be much easier if we’d stop relying on measuring cups and start using the scale. But since the old volume system of measurement is still pretty standard, we’re using it along with weight measurements, which you can use in this and most other American cookbooks.
Hope it helps.