Unfortunately, there is no single exact, correct answer to that question for dry ingredients, as a cup of all-purpose flour will weigh different amounts depending on how you measure it into the cup (i.e., if just spooned in, you'll get less by weight than if you spoon it and tap it down before leveling, as the tapping compacts the flour). Likewise, granulated sugar weighs less than flour, etc. etc. We actually have a post on this topic as it relates to flour measurement (look about mid-article for the relevant area of the post): https://cookieconnection.julia...olbox-talk-flourpost.
If a recipe does not specify how the flour was measured or does not provide weight measures, you'll probably need to test it and establish your own right amount of flour for the recipe. Alternatively, find recipes that already have weight measures (mine all do) and don't mess with the conversions.
Flour is the biggest issue; more standard conversions exist for things like salt, spices, and liquids.