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Anon is a physicist
(sh.itjust.works)
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But it does affect the downward force acting on the object. Given two objects of the same shape but with different masses, one will indeed fall slower than the other. This is because the ratio of weight to surface area differs a lot between the two. Here's a calculator from NASA you can play with, and a relevant passage from the same page:
https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/termvel/