I did some more research after posting. Specifically, it's Polygonum caespitosum Blume, or Oriental Ladysthumb (also known as Knotweed, as you correctly noted).
I learned quite a bit about plant identification and its associated terminology while looking this up. If anyone cares, the link is here:
http://plants.usda.gov/java/profile?symbol=POCE4
Knotweed by: Grambo
Appears to be Pink Knotweed. Also called Pennsylvania Smartweed, Pinkweed. Prop. name: Polygonum pensylvanicum
I've never really considered it to be a weed, unless it gets in my veggie garden. But, that's just me.
