Top Law Schools

I got offered a Hamilton this cycle and realize that this is already an unbelievable deal, but at the risk of sounding extremely ungrateful I was wondering if anyone's known Columbia to give need-based aid on top of the Hamilton (which covers tuition) to help with housing/books?

No. The Hamilton is as high as Columbia goes. I believe that NYU similarly does not award anything over full tuition (there are a few programmatic scholarships that include some research funding in addition to a tuition waiver, but the research funding isn't a "stipend" per se). However, Chicago's Rubenstein (a.k.a. "Ruby") does include a stipend. This is why the Ruby is often referred to on TLS as the best deal anyone could possibly get for law school. (Provided, of course, that they're willing to attend law school in Chicago!)

You're expected to make a substantial financial contribution under all law schools' financial-based regimes, with the understanding that you'll have either a big salary or LRAP coverage waiting on the other side. A full-tuition scholarship means you're already paying less than the expected maximum, so it makes you ineligible for need-based aid under that philosophy.