RE: CHECKING THE C.G. OF A NEW PLANE?
Most people would balance with the fuel tank empty.
The purpose of this is cause while you fly the engine is
using fuel inturn making the plane lighter in the nose.
So lets say you did balance it with the tank full. When the
fuel gets low you loose weight in the front(nose) and it would make the
plane tail heavy. A plane is better a little nose heavy than tail heavy
most generally.