With the TT we had, we never carried any water in it. Our style of camping then was with hookups. We always had a destination at the end of each day. Actually, there was only one time of traveling that we did not go from one destination to another in one day. We broke that return trip home up in 6 hr increments (2 days), but we had reservations for that one night at a full hook up. Being that it was a TT, it was very unlikely that we were going to go inside it while traveling to use the restroom. First of all, we would have to stop. Where we stop, there would be a bathroom with A/C. TT wouldn't have A/C on. So it made no since to us. The only time the pump came on in the 3 years of owning the TT was to winterize it.
But, now that we have a motorhome, and its more feasible to use the restroom and/or stop with out hook ups, then we will try and keep it full as much as possible. It's only got a 40 gallon tank on it, so the 350lbs is not going to make much difference to it.