Why not weigh the aircraft before departure? Doable, nowadays
These days it's possible to build a scale that would fit under the wheel contact area and handle the range of weight expected -- all solid state, no springs or balance levers. Why not have a little square cut out of the pavement at each aircraft gate on which the wheels of the various sized aircraft will rest, instrumented, to measure the weight on that area? Turn on the ones for the specific aircraft, make sure it's parked within the painted lines, sum the total weight. Ding! Why (rolls eyes) I can't imagine why any airline wouldn't want this information .... Wrong topic, just mentioning it's doable nowadays. The rocketeers must do this, they really need to know exactly what their rockets weigh before they launch them.