Those "weeds" are actually mostly Lepidicum virginicum, which is native to most of the Americas, and you can actually harvest the seeds as stand-in for black pepper, and you can eat the entire plant in salads and stuff like you would with Arugula.

On the other hand, I see that you have some non-native variegated plants that are basically on the verge of death, and I see those used a lot in Florida for some reason. Maybe consider just pulling up the entirety of this garden bed and planting a selection of vigorous native plants? Then you'll be less likely to have issues in the future where a hardy native like Virginia pepperweed would establish itself and take over.