There is no good reason to run around empty. The amount of extra fuel needed to get the extra weight moving is not worth talking about. Likewise extra braking to stop it. What weight in the tank does help is add stability, especially in windy conditions or if you go into an exit corner a little too fast. Lowers the center of gravity of what is mostly a box full of air, most likely with heavy stuff like a loaded fridge on one side.
If I know I am going to be dealing with wind I try to be full. 100gal/800+# for me. If I know I will be dry camping or a night at Walmart on the way somewhere I have water onboard accordingly.
