I used to fly on P'3 Orions when I was in the Navy. Our flight engineer would calculate "Weight and Balance" as part of his preflight.

The engineer's calculations would start with the dry weight of the plane (about 65,000 lbs). Then he would add the weight of fuel, about 200# per passanger, then other weights for additional items (luggage, torpedos, etc.). He even had a specialized 'whiz wheel' (slide rule) to help figure this out. About the only thing that would change were people moving around (taken care of with the trim tabs and autopilot) and the burned-off fuel. Oh yeah, dropping a torpedo would make a difference too, but the trims helped there too.

I imagine that it's pretty similar for airlines, large and small.

Just my input.

Bob