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Yours might be weeds--I'd start a new thread and post some pictures to find out for sure which species you have. This particular species might not be a weed, but there are other Polygonum species that can spread quite aggressively so if you have one of those other ones then you're doing the right thing by pulling it.
This plant is definitely very polite; not at all aggressively spreading. I think I will leave it where it is to carry on its merry existence. Thank you!