how can you weigh a plane without using a scale?

Answer 1

if you know the weight of the metal used and then how much of it was used you could calculate it and the same for all the non metal parts

Answer 2

You could estimate the plane's empty weight as follows:

Figure the passangers weight at 170 pounds each.

Multiple that by 2 for a short-distance prop plane.

Multiple by 3 for a medium-range plane like a 737.

Multiple by 5 for a very-long range plane like a 747-400.

The longer the range, the larger fraction of weight is fuel.