Well, thanks everyone. Perennial peanut is a ground cover (it's also called ornamental peanut), so the goal is that once it gets established, it will smother everything else. But since it's been planted in plugs (they sell it in rolls like sod, apparently, but this is a different species), there is still some bare ground in between them. It is that bare ground that is being coated by weeds (some of which, like grass, wouldn't be "weeds" anywhere else). So, I think I'll continue to pull the weeds (it's only a small backyard) and just leave them where they land.
