My guess would be spurge. Pigweed is a succulant, also known well as Purslane.. I happen to have both in my lawn. I had it looking great this summer till a long dry spell in june. The grass recovered but not before the spurge and pigweed took root.
I find if sprayed early, it keeps it at bay. Once it takes good root and has a chance to flourish, forget it, try again next summer.
My lawn guy uses Eliminate. Great on all this stuff IF like arjedi said is used below 85 degrees when the lawn is not under any stress. I sprayed a month ago at around 80, and i regret it now. I have spots where the weeds died, but took grass with it kinda. Now the patches of bare lawn are becoming host to the same crap i killed initially. It's a loosing battle. I'll try again next summer.
Without irrigation, its very difficult to keep my lawn nice. Worst part is, i only have at most 3" of topsoil over hard shale so it makes it impossible to retain moisture for long, and irrigation isn't an option due to impossible digging.
SIGH.
Edited for spelling and to add, A mature purslane plant can make thousands of seeds over the course of a summer, and the seeds remain dormant and potentially active for up to 30 years in the soil. Aye aye aye!