Purple loosestrife.

Roots are just part of the problem - one plant can produce up to 2.7 million seeds which is why it's choking up so much space along the nation's lakes, ponds, and waterways.

We've got a lovely little meandering creek across the street and down a slope - every year one of us in the neighborhood dead heads the few we get and shovels up the obvious plants that we see so it's never gotten much of a toehold along our stretch yet.

Nothing I've grown before, but it looks like Polygonum persicaria to me.

Donna, I think you might have steered me in the right direction. It really didn't look like Purple Loosestrife and it wasn't quite Polygonum persicaria, but that one looked pretty close. I ended up looking up Polygonum plants in this area and came up with Persicaria amphibia - Water Smartweed. I'm not an expert, but I'm pretty sure that's it. Apparently it's a native.

Polygonum

The Persicarias were formerly named "Polygonum."

So for the Smartweeds/Lady's Thumbs/Tearthumbs/etc., anything you see as "Polygonum ------" is now correctly named "Persicaria -----."

Persicaria amphibia, aka water smartweed. As might be determined by the species designation, a water plant. A serious spreader but a native plant so not considered invasive.

Thanks for verifying, Gardengal48!

Thank you all for the help! I've been on a kick lately to identify anything interesting that I find.