I am looking for advice on how to control or eliminate virginia buttonweed (diodia virginiana) from a lawn that is a mix of st.augustine and bermuda
grass... I have cut back watering to a minimum since the weed thrives in
wet conditions and continually remove the weed by hand but these methods
do not effectively stop the spread. Any tips on this subject?

For a look at this weed, click here

http://www.ppws.vt.edu/scott/weed_id/diqvi.htm

I would try spraying full strength household vinegar as a foliar spray first. If that doesn't work after 3 days, then try adding a little orange oil to it and spraying again. If that doesn't work, go to 20% acidity vinegar. Be careful with that strong stuff. If you get in your eyes you will be blinded for months or longer. I use it regularly and have had no problems but if you're a little klutzy, wear a full face mask before pouring into a spray bottle.

Then if the 20% doesn't work, add some orange oil to that (3 ounces per gallon).

Best results from vinegar come from spraying in the heat of the day. I realize we don't have that much heat anymore, but do what you can.

Vinegar is nonselective and will kill with overspray. Do your best to keep it on the weed and off your grasses.