Might be Chamaesyce nutans (aka Euphorbia nutans), common names are eyebane or nodding spurge. As the common name suggests, if it is eyebane, don't get the sap in your eyes!
hortster

You're right... it's Spurge. Funny... I've heard of Spurge, but didn't know it was such a ferny, dainty, pretty little thing. Sigh. Now off with it's head. (And roots)

"Spurge" includes ever so many plants in the Euphorbia family. Not all of them are quite so dainty. I agree these little guys can be interesting to look at, but they sure can spread!

They sure do! I've been pulling out weeds by hand for days now, buckets and buckets of weeds.

This is the time of year for lawn weeds! I compost a lot of mine, if they haven't bloomed by the time I get them pulled.

I eventually will want to start composting, but right now I'm not sure where in my yard to do it. I don't want to SEE it from the pool or patio, and both sides of the house have other reasons they might not be ideal locations for composting. I'll have to get moving on that, though. The Live Oaks have started dropping so many brown leaves, and there will be MOUNTAINS of them soon.