An influx of deep moisture from the Gulf of Mexico (partly residual moisture from former Tropical Depression #4) and an upper-level low just north of the Yucatan will keep a good chance of showers or thunderstorms in our picture through early next week.
The National Weather Service is calling for P.W. (Precipitable Water) values of around 2 inches locally, which indicates a deep pool of moisture. Basically, P.W. shows the amount of moisture above a given locale. Often rain amounts can exceed the total P.W, value as water vapor flowing in from the surrounding area can increase rain potential. However there is a general correlation between P.W. values and precipitation amounts.
The waxing and waning of P.W. over certain areas can be tracked. This loop shows a loop of current P.W. amounts. You can see a surge of deep moisture passing through the Bahamas, and then Florida and now moving into the eastern and central Gulf: http://tropic.ssec.wisc.edu/real-time/mimic-tpw/natl/main.html.
The moisture flow can also be tracked on a water vapor loop, which also shows the upper-level low off the Yucatan.
At any rate, expect rain to hang around awhile longer with a 40-50% chance for thunderstorms through the weekend.
Rainfall amounts should be fairly modest, though totals in excess of 1 inch may be common over inland parts of Galveston County as afternoon heating enhances atmospheric instability.
Here is a link for those wanting to know about precipitable water: http://www.theweatherprediction.com/habyhints3/899/