Hi there twitcza! I was actually in the same situation as you a few weeks ago. I was accepted from the waitlist at BC and had to decide between going there at full sticker or going to another Boston law school with a substantial scholarship.
I don't think it hurts at all to ask BC for money. I recently contacted the financial aid office about this myself, and I actually have a few forms to fill out first, but they were very helpful and I can't imagine they would give you a hard time if you asked about extra funds. However, as we were both accepted off the waitlist, I have to imagine that they have already dispensed most of their financial aid to students that were admitted via early or regular decision. Also, I also think that if they have extra money, they would offer it first to people who they feel may be deciding between BC and another school so as to further entice them to attend BC. With us, we know we're lucky just to be there, so I'm not sure that we would be a priority if BC has extra financial aid to dispense. So, my advise would to be to definitely contact them if you're unhappy with your financial aid package, but don't be too surprised if they can't add any funds to your package.
I've not done any research on Chicago-Kent, but my biased opinion is that BC is awesome, so I would definitely recommend coming to the Heights in the fall. Also, if you're worried about debt, BC is apparently a great school for future career prospects (their website says that Princeton Review named them one of the top five law schools for career prospects, and a recent law.com article showed that BC sends ~ 1/3 of their class to the "BigLaw" firms that everyone seems to want to work for).