When it comes to liquid measure, there is a close correlation between weight and volume. You'll rarely see a recipe in which the liquid ingredients are listed by weight, however, unless you're using a professional recipe. Dry ingredients are troublesome and need weight measures. As a cooking teacher, I tell home cooks that if they want to become better cooks, they should get themselves a scale for dry ingredients. The more space there is between the particles of flour, grains of rice, or chunks of chocolate, the more air there is in the measuring cup and the less actual ingredient.
Chopped nuts take up a lot less volume than whole ones.
If you sift the flour before measuring it, the flour will be fluffier, more aerated, and therefore will take up more room. If you scoop the flour straight from the bag and tap the measuring cup so the flour settles, it will be very compact, and you'll get a larger amount of flour in the cup. The exact wording of a recipe has important clues about how to measure ingredients. For dry ingredients, the weight usually does not correlate with the volume, as it does with liquid, because the density of dry ingredients is usually lighter than liquids and it varies a lot more. One cup of fresh breadcrumbs might weigh only 3 ounces.