Hi Richard,
I don't see your profile as "weak" academically at all, unless your undergraduate GPA is low (you only mention your Masters) or your undergraduate institution is considered too light-weight. Actually, lots of successful applicants to top MBA programs have liberal arts backgrounds -- business schools appreciate the diversity of perspective you bring to the program.

The challenge will be to show that you have, or are working on building, the quant competence to keep up with your classmates. If your GMAT is unbalanced (i.e. low quant, high verbal), you'll want to address that in practice by taking coursework immediately to build up your skills, starting with calculus and statistics. Courses in finance could also be added, but if you have a low quant GMAT, take the quant fundamentals first. You can use online courses such as UCLA's highly regarded business extension classes, or take classes locally, whatever works best for you.

You will also want to define very clear post-MBA goals, so that the schools you apply to can really see that you know why you're taking this step now.

Good luck!
Margaret Strother