Why Does Water Leak From The Overflow Valve On My Water Heater?

Valve sounds like its going bad or may have a piece of dirt caught in it. Open and close it a couple of times and see if that helps, if not then replace it

First thing is, you never just open and close a t/p valve cause then it will always leak. Could be your expansion tank (if equiped) is bad or your well tank is bad or the city worked on the lines and if you don't have a pressure reducer valve could have overpressurized the tank. Gas valve or t-stat may be bad.  T/p could be bad. Most common two are t/p is bad or expansion tank is bad.