Full or nearly full here. I have not noticed much of MPG difference.
Depending upon your configuration, a full tank may make the TT more stable in winds. A lot of weight low and directly above the axles. My rig has very little difference in hitch weight full or empty, but pulls a whole lot more stable. Also, you never know when you must make an unplanned overnight in someplace dry.
Just because a CG water supply meets health and safety standards does not mean it tastes good. Plenty of times I found the water undrinkable because of minerals and smell.