Here is a better picture of it...

I dug some up and planted it into a container, and now I am watering it. It has tiny yellow flowers.

Bob, thanks for the better photos. I did browse photos on several of the Wildflower sites for Arizona, and didn't find a match. If you don't get a response here, you can get an ID by sending a note to the University of Arizona Herbarium. They have more than 420,000 specimens for reference, and part of their mission is to provide the public with plant identification services, free of charge. They would appreciate good photos of the flowers and leaves. They also ask for location (i.e. residential Phoenix), cultivation status (i.e. volunteer in yard), flower color, size, leaf arrangement etc. I would send the email request to the Herbarium Director, Shelley McMahon, at mcmahonm@Arizona.edu, and ask her for forward it to the appropriate person for response. There are also additional resources available at their site: University of Arizona Herbarium.

This approach works well for any state, since they all have herbariums. Those herbariums are typically funded by government grants, so all should have free identification services. For example, if you search for Arkansas Herbariums, you may find there are about 8 in existence. Some are in State offices, and others are at Universities. When there are multiple choices, I usually choose the one that has the most herbarium specimens on hand (suggests that their resources will be good).

Once you determine species, please post back here.

Okay, thanks for the info. I will try that and post back here if they figure it out. At times, with enough water and full sun, it looks like an attractive ground cover option. I'm going to try growing it in this container in full sun, and give it water twice a week, and hopefully it will turn into a nice specimen plant.

They seem to be perennial here. But they only flower when it is warm or hot.

One thing I noticed is that it seemed to first appear on the scene right after I planted a moringa tree that I bought from a nursery in a one gallon container. I wonder if it hitched a ride from the nursery to here?

Do those flowers really have 3 petals? Or are they just scruffy four petals?

I think they have 3 petals, but I will look closer today and report back.

3 would be very unusual. I suspect there may be runty extra petals somewhere.

After looking at it with a magnifying glass, as far as I can tell, it has 3 petals, but the flower is weird looking. The other petals might be obscured by other parts of the flower. This weird weed seems to have everyone stumped. Nobody knows what it is.

Your expert botanists at the University of Arizona herbarium will know the plant. Have you sent them the info??

Yes, I have emailed them the pictures, but have not heard back from them yet. I will post their response here when they do respond.

Thanks for returning with this information.