@Suki, can you take a piece to your local nursery/ Maybe they will have a clue. Or they county extension agency.
If you take it in, I would suggest the piece like the first picture, many weeds look alike on the surface but the crap under the ground is what tells you for sure what you are dealing with.
Remember a "Weed" is just a plant you don't want there.
If you want it there you can wait for it to bloom (if it does) and enjoy it.
Nothing wrong with that. My visiting birds sow a lot of things that way.
And I can't ID it.... If you get stuck I'll ask my nephew though.
I really do need to ID it....
Also, many so-called weeds are Herbs
I have to agree with @freeofgod, root spreading weeds are some of the most difficult to rid yourself of. Early eradication and repeated maintenance will slow them down, but seldom eradicate it. They store energy in their roots and will go dormant if they are repeatedly eradicated on the surface, but you have to remain vigilant for their return.
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