These are likely chamberbitter or gripe weeds (Phyllanthus) and they are a very common summer annual weed in our area. It has become more common in southeastern Louisiana over the last 10 years or so. Indeed, it is now one of our most significant summer weeds. You may not ever totally get rid of it, but you can manage it.
In beds: This summer annual weed can be controlled in beds by hand weeding the bed or using a nonselective herbicide. Hand weeding works well because there are no below ground bulbs or rhizomes to resprout.
Where you can apply an herbicide just to the foliage of the chamberbitters without getting it on the nearby desirable plants, you can use glyphosate (Eraser, Killzall, Roundup, Grass and Weed Killer). Use a shield when spraying or cover nearby ornamentals with plastic sheeting or bags to prevent the spray from getting on them. If the herbicide gets on the foliage of desirable ornamentals it will damage or kill them.
Once the weeds have been cleaned out of a bed by hand weeding or glyphosate, thoroughly mulch it with two inches of mulch to minimize new weeds showing up. The mulch will suppress the germination of the chamberbitter seeds in the soil. The thickness of the much is important for effective control.
Chamberbitter does not respond well to some preemergence herbicides, but isoxaben is recommended in some publications. After hand weeding or killing with glyphosate, apply a product containing isoxaben (such as Green Light Portrait Broadleaf Weed Preventer) following label directions. But, two inches of mulch will also do a good job suppressing weed seeds.
In the lawn: If you have St. Augustine, centipede or zoysia, spot treat with Atrazine during the summer. It is too hot to apply over the entire lawn, but you can spray spots or patches of the chamberbitter weeds where they occur. Make two applications following label directions. Atrazine also serves as a preemergence herbicide, so the areas where you have treated twice should not see much regrowth (do not use Atrazine in beds).
For best control, spray the lawn with Atrazine in early to mid-May before it gets so hot. Then, spot treat during the summer if needed. Isoxaben (see above) could be applied to the lawn in early summer as a preemergence herbicide to prevent seeds of this weed from sprouting and growing.
Also, mow your lawn at the highest recommended height to make it more competitive – St. Augustine at 3 inches, centipede and zoysia at 2 inches.
A bad chamberbitter infestation in a lawn may indicate a lawn that is in poor vigor. Chamberbitters have a harder time establishing in a thick, healthy, vigorous lawn. Make sure you provide your lawn with proper care (mowing, watering, fertilizing, sun) to minimize chamberbitter problems.
Consumer Horticulture Specialist