After seeing the little yellow blossoms on my mystery plant, I couldn't help but think that it looked an awful lot like an abutilon. So I did a little Internet surfing and I think I finally have a name: Abutilon theophrasti (common name: Velvetleaf). Most of the sources I found identify it as a noxious weed in many parts of the country, particulary in cornfields where it steals water and nutrients away from the corn. But others indicated that, although it can reseed freely, if you collect the seedpods you can control it.
So now the question is: Do I yank it, re-locate it, or just leave it?