The main problem is that Aristotle tends to get badly misreported on this subject. He did make a couple of errors in what he wrote about rate of fall, but he didn't claim that rate of fall is proportional to weight: his mistakes are a bit more subtle than that.

But that doesn't stop the critics. If you go to Quora you'll find people claiming that Aristotle said rolling objects stop because they get tired. You can find Stephen Hawking claiming that Aristotle

invented a new principle -- that bodies proceed more jubilantly, and hence accelerate, when they come closer to their natural place of rest.

And you can find Galileo himself claiming that

[Aristotle's] language would seem to indicate that he had tried the experiment, because he says: We see the heavier; now the word see shows that he had made the experiment.

(Galileo, The two sciences, p. 62 in the 1914 translation by De Crew and Salvio; = p. 63 in the 1638 Italian edition.)

Now, to be fair, Hawking didn't make up the 'proceed more jubilantly' thing himself. He copied it from the historian Herbert Butterfield (The origins of modern science: 1300-1800, 1959, p. 6). So we can't accuse him of fabricating libellous statements: he was just lazy and didn't bother to check if Butterfield was telling the truth.

Because he wasn't. It's made up. Aristotle never said any of these things. (Butterfield's fiction is a bit ironic, given that Butterfield himself was a key figure in critiquing the notion of teleological history.)

The thing about rate of fall being proportional to weight is Galileo's extrapolation from what Aristotle says. Now, it is a logical extrapolation, if you ignore some things that Galileo knew but which hadn't been discovered in Aristotle's time. But even then, Galileo doesn't report Aristotle honestly. At no point does Aristotle say 'we see the heavier': Galileo made that up. And when Galileo goes on --

But even without further experiment, it is possible to prove clearly, by means of a short and conclusive argument, that a heavier body does not move more rapidly than a lighter one provided both bodies are of the same material and in short such as those mentioned by Aristotle.

That's even worse: heavier and lighter bodies provided both bodies are of the same material is almost opposite to what Aristotle describes.

Aristotle's thought process becomes extremely clear if you read what he actually wrote.

Language recognizes (a) an absolute, (b) a relative heavy and light. ... Our predecessors have not dealt at all with the absolute use of the terms, but only with the relative. I mean, they do not explain what the heavy is or what the light is, but only the relative heaviness and lightness of things possessing weight. ... By absolutely light, then, we mean that which moves upward or to the extremity, and by absolutely heavy that which moves downward or to the centre. By light or relatively light we mean that one, of two bodies endowed with weight and equal in bulk, which is exceeded by the other in the speed of its downward movement. Those of our predecessors who have entered upon this inquiry have for the most part spoken of light and heavy things only in the sense in which one of two things both endowed with weight is said to be the lighter.

(Aristotle, On the sky 308.a7-b2, trans. J. L. Stocks.)

Now, Aristotle was definitely wrong in thinking that there's such a thing as 'absolutely light' or 'absolutely heavy'. But look at the sentence about relative speeds carefully:

By light or relatively light we mean that one, of two bodies endowed with weight and equal in bulk, which is exceeded by the other in the speed of its downward movement.

That's where Galileo's idea came from. But he doesn't write that

a heavier body [moves] more rapidly than a lighter one provided both bodies are of the same material

as per Galileo: he talks about two bodies of different weight but equal volume.

And this is an absolutely accurate description of the difference between heavy and light objects in a medium -- that is, it's an accurate description of buoyancy. And buoyancy absolutely is proportional to a difference in weight.

So Aristotle's fault is really that he didn't know the difference between gravity and buoyancy. The principles of buoyancy hadn't been discovered. That had to wait until Archimedes came along. Archimedes ought to have been able to make the correction, but as far as we know he didn't. That's why we had to wait until Galileo. And of course Galileo's finding is correct, even though he distorts what Aristotle says. It may be that he, like other westerners of his time, had to rely on inaccurate Latin translations of Aristotle, instead of on the original text.

Aristotle does make mistakes in this passage, but they're a bit more understandable than the usual picture of him, as someone making dictatorial pronouncements about rate of fall being proportional to weight. His actual errors are (1) there isn't actually any such thing as 'absolutely light' (he thought flames were an example of something absolutely light), and (2) buoyancy isn't the same thing as gravity.

There's so much misreporting of ancient science in modern books that it's normally best to assume they're false unless they cite specific passages in specific ancient sources. Aristotle does make mistakes, but often not the ones that he gets tarred with. I give a few additional examples of that and some more sources in this online piece I wrote a few years ago.

Hey there,

Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.

If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!