This question is more a brainteaser and it's less about the actual weight but rather about how you will measure it.
You can use both non-creative and creative approaches:
1) You can weight each part of the plain separately: wheels, chairs, etc. Don't forget the paint
2) You can recommend tying a rope around the plane’s midsection, throwing that rope over a rafter at the top of the hangar and then attaching the other end of the rope to a large platform onto which you will quickly load bricks of a known and pre-defined weight until the plane lifts off the ground and then all you need to do is count the bricks.