Here's a consideration I haven't seen yet:
Before making the decision of full, empty or partially full, owners really ought to understand their water tank. Years ago, water tanks had baffles in them that reduced "water splashing" or "water movement" inside the tank. Those baffles more or less kept water "still inside the tank"... Back then, it really didn't matter much whether you towed with a partially empty tank or not because there was limited water movement inside the tank.
Those "molded in baffles" took up space inside the tank which reduced capacity or meant a larger tank to carry the same amount of water. As manufacturers started building smaller, ultra-lite trailers led to the need for lighter tanks that carried the same or more water than before, so the baffles started to get smaller or they were eliminated completely. Thats when people towing with half empty tanks started noticing increased sway in some rigs, they also started having "tank problems" like broken straps, tanks falling out of position and split/ruptured tank walls...
Why? A 45 gallon water tank carries about 350 pounds of water (more or less). If the tank is full, that water is essentially "static even when the trailer is moving. But, a half full tank with no baffles, has about 175 pounds of water, swaying back and forth as the trailer moves down the highway. Increase sway, you increase water movement. Sooner or later, you get to a point where you have 175 pounds of weight "slamming against the tank walls" and changing the "balance of the trailer"...
If the tank is in the front of the trailer, there's less movement and the sway is not as noticeable. Same with tanks positioned above the axles. That "slamming back and forth" is not as noticeable and trailer sway isn't greatly affected. On the other hand, if the tank is located in the rear of the trailer, that sloshing is increased. Depending on the rig (tow vehicle, hitch sway control, cargo loading) sway can be "not noticed" or can make a trailer "**** to control on the highway"...
Why? sway induced inside a half full water tank with n o baffles. A few years ago, we had many more reports of broken tank straps, damaged tanks, etc. Keystone didn't start using baffled tanks again, they just changed the mounting system to keep the tanks in position better. We still have "175 pounds of water slamming into the tank ends when we tow with a half full tank"...
Some rigs, depending on how they're set up, will notice that weight in handling difficulty, some better matched tow vehicle/trailer combinations won't notice increased sway at all... But, if you tow "half full" with a tank that doesn't have baffles, you will have an increased possibility of water movement that could damage your tank installation or the tank itself.
How to eliminate that water movement? Tow with a full tank or with an empty tank.