If anyone can help I will be most grateful! I've been fighting this weed in my beds for years and it just keeps coming back!!!

Because you haven't had any responses, I thought I'd try to look up your plant in my weed book (Weeds of the Northern U.S. and Canada). Because you're in Georgia, maybe this is a species that wouldn't be covered but here are a couple of GUESSES: small snap dragon? blue-eyed mary? Have the plants flowered since you took the pictures? It looks like maybe there are some pinkish buds in the pictures but I can't be sure.

They do eventually flower, so you want to pull them up before they make lots and lots of little mare's tail seeds. They some right up, so it's not too bad.

It's one of the nutsedges. A ROYAL pita, believe me.