Galileo Galilei discovered by experiments that all bodies tend to fall with the same rapidity (I use it in an intuitive sense, you can replace it by 'acceleration' used in today's physics language), independently of their weight. He also provided the following rationale, based on the proof by contradiction (I do not have the original wording at hand, but I believe I can paraphrase the idea, which I am interested in.)
Let's imagine one heavy body and one light body. Suppose that heavy bodies fall faster than light bodies, as almost everybody believes. Connect the two bodies so that they form another body. This resulting body is heavier than the original heavy body, so according to the assumption it should fall faster. But on the other hand, the original heavy body is being inhibited in its fall by the connected light body, since this "wants" to fall with less rapidity. Due to this inhibition, the heavy body part should fall with less rapidity than it falls normally alone. So we arrive at contradiction, and the only way to resolve it is to reject the assumption. Instead, all bodies fall with the same rapidity (acceleration).
What do you think of this argument - is it valid, or no? For what reasons? It is very compelling at first, but on the other hand, should not the law of free fall be experimental law, rather than logical necessity? If so, where is the problem with the reasoning?