I am in North Florida and have many of the weed shown in this link:

http://apalacheehills.com/Weeds/stemFlowerWeed.html

Note the small white, ball-like flowers near the stem. It produces a lot of seeds, and spreads rapidly.

If you click on a photo, it will enlarge. This weed grows from spring to fall. I have checked in weed books and cannot find a matching photo. I have also checked at 2 local nurseries and the county extension service. Everyone has seen this plant, but nobody knows its name. Does anyone know what it is?