I haven't seen it said specifically, so, the reason you balance with an empty tank is that as the tank empties, the CG moves back. Planes fly ok a bit nose heavy (from the fuel being added forward of the CG), but some planes can become unstable if the CG moves back too far. So, if you balance right "on the edge" with a full tank, as the tank empties, your plane may become unstable.

If you have a pusher or other oddball arrangement that puts the fuel tank behind the CG, then you balance with a full tank.

Many flying wings have the tank on the CG since wings tend to be much more sensitive to CG than conventional setups and even a small CG shift can be have a noticeable effect on performance.

If you want to run huge amounts of fuel, it's not uncommon to have a header tank close to the engine and a larger tank on the CG, or to use a pump such as the perry mico-oscilating (sp) pump.