Auntie: I'm sure, given your growing climate, that pretty much most things that grow on the planet could be considered a "weed" where you are. However, in my part of world, there are only 100 or so plants classified as "noxious" that actually manage to survive our winters. Believe me, prickly pear cactus is a BIG deal in these here parts lol. I envy you : )
This is one (of millions) of plants that will not survive as a perennial here. I "winter" mine inside the house. Am always amazed at how "valiant" some of them are lol

Artichokes