MSAR says 70% receive aid, although I'm not sure if this includes loans. Average graduate indebtedness is $145,653 which is great for a private school and comparable to Columbia. They offer merit and need-based scholarships but I have no clue how the dollar distribution between the two is. Lastly, I will add they have the best subsidized housing in NYC and a primary care loan repayment program (up to $80,000 if you work primary care for 2 years in and undeserved area after residency). I believe this is a very commendable program and more schools should apply their aid money in a similar fashion.
My overall opinion on financial aid at the Manhattan privates: NYU>Columbia=Sinai>Cornell