Atwood water heater....1998 vintage so it is most likely a 1/2" NPT threaded relief valve
Couple of things.....
Doesn't look real bad...crusted up etc
With water supply on....pop open via lever and blow out seat/disc...could be scale built up
CAUTION: Water could be HOT and it will really blow
Weeping can be due to loss of Air Pocket
Air Pocket naturally forms in top of tank when filling but can be lost ---gets absorbed into the water or purged off
Air Pocket controls pressure increase when heating water. Water swells when heated and W/O air pocket the pressure can increase enough to cause T&P Relief to weep
Water doesn't compress...air does
To establish air pocket
Turn Water Supply OFF
Open nearest faucet (hot side) to relieve pressure
Open T&P Relief via lever......hold open until water stops running out then let vlave snap closed
Close faucet
Turn on water supply