Wealth is obviously correlated with things like past donations given, legacy status, and access to better educational resources. And if you're looking at people coming from, say, an elite preparatory academy, wealth can't be the only disparity, because a poor person would have to be on a merit scholarship to that academy in order to attend.

If you take away all of that, though, and you show someone at Harvard Law admissions a poor applicant and a rich applicant from Princeton, both with LSAT scores of 176 and GPAs of 4.0, it's much more likely the poor applicant will be accepted.

I think it scales downward, not upward; I think it's more accurate to say "your chances improve as you grow less wealthy," not "your chances decrease as you grow wealthier." The baseline isn't set that high. An absurdly rich person probably doesn't have a markedly different chance of getting in from a very rich one. A person from a lower-middle class family has a better chance than either. A person from a family below the poverty line has a better chance still.

EDIT: Again, of course, all things being equal. Which they rarely are. But a poor person with good grades is practically a shoo-in at most law schools.