I don't usually travel with a full water tank, but that is mostly due to where the tank is on my TT. It is in the front left corner of the trailer. 30 gallons of water all in one spot.
When I do travel with it full, I try to move some weight to the other side of the trailer and tighten the weight distributing bars a bit.
I've not run into the situation of having to fill while on the road, but what about "camper friendly" stores like Walmart, Cracker Barrel, Cabela's, etc?
Also, if you ask at a gas station convenience store, remember to BUY something in the store -- long time ago a friend owned a convenience store, and he hated when people came in asking for directions or anything else without at least buying a cup of coffee. Heck, at a gas station, top of your fuel tank and then ask about filling your water tank.