I'm thinking the most bang-for-your-buck upgrade is wheels. Most bikes, expcept for the super high end ones, come with pretty mediocre wheelsets. You'll probably be able to lose the most weight there and have smoother running hubs. The drawback to that is that good wheelsets are generally pretty expensive.

I quizzed my husband about other parts and we came up with - saddle, unless you've already replaced it. Stock saddles are often pretty awful. Rear derailleur - having a nicer rear derailleur can make your shifting better. Brakes - a lot of bikes come with the cheapest possible brakes too. I know that on my old Fuji I really hated the brake set it came with, they were grabby, not at all smooth.