Actually what the illusion I linked to shows is that we "perceive" density by estimating it visually, and this can trump what our muscles and skin tell us about

Actually what the illusion I linked to shows is that we "perceive" density by estimating it visually, and this can trump what our muscles and skin tell us about the weight of the object by means of pressure. So the answer is "both": we estimate density and weight, and what we perceive is a combination of the two, adjusted (biased) by our priors. Specifically, a larger object with the same actual density but the same visual appearance will feel "lighter" when compared. And it's a very strong illusion, in the sense that it works even if you know what's happening.. it's very hard to shake the feeling that the larger object is lighter even though they actually weigh the same.