Galileo's argument is actually quite slipshod and is based on the ambiguity of language and the narrowness of what-we-commonly-experience as a slice of all-that-really-is.
If Aristotle were right then the rocks would EITHER fall slower or faster together. There is no "knowing" if they are one object or two.
But Aristotle is wrong. Which means Galileo's thought experiment is irrelevant to reality and should be ignored. The picture is very simple: gravity pulls down, air resistance pushes up. Gravity is constant but air resistance is higher for faster moving objects. That's all you need.
There is nothing wrong with assuming something that is false. Doing so and coming to a contradiction is a common way of disproving the premise.
Also, you missed the point. The premise is that heavier weights fall faster. The cleverness in the argument rests in consider what happens when you break a heavy rock into two differently-sized pieces. Using the premise each should fall slower than the whole; but what changed? Do they somehow know that they are separated? Of course not, that's nonsense. There is no "knowing" if they are one object or two. Therefore everything falls at the same rate. Which is true assuming no atmosphere.
The argument is still valid in the presence of an atmosphere, all you have to do is ensure similar drag coefficients.
If Aristotle were right then the rocks would EITHER fall slower or faster together. There is no "knowing" if they are one object or two.
But Aristotle is wrong. Which means Galileo's thought experiment is irrelevant to reality and should be ignored. The picture is very simple: gravity pulls down, air resistance pushes up. Gravity is constant but air resistance is higher for faster moving objects. That's all you need.