Epilobium species, WIllowherb. I don't know which ones you'd have in your area. The common weedy one here is E parviflorum.

epilobium

Those that disguise their way up through other plants and reach some height....the deer will eat ;-) You'll hate yourself if you let them flower and set seed.

I don't think I've let them flower, but I already hate whoever did and gifted me with an endless string of seedlings! Maybe my property will eventually run out of seeds and the infestation will slow down...

Not unless there is a wide "dead zone" around your property :-) Many weed seeds just blow in with the wind.........the epilobium is just one that will do so.

There's a wide "crowded out by much larger invasives like blackberries" zone around my property. Does that count? ;)