In addition to total weight, there's also a balance issue for all aircraft.
I spent a lot of years in the aerospace industry and the final few years were spent in sales and marketing of portable electronic aircraft scales.
All aircraft have to be weighed every few years to verify the center of gravity (CG) is still within the specified envelope. Every change made to the aircraft can effect the CG - seating layouts, re-engine, paint, instrumentation, weapon loads, etc.
For instance, the CG of an F-16 has to be within a 16"-long envelope along the centerline of the aircraft. Helicopters are also especially critical.
