snowfalcon2
Also please consider that only the passenger weights are unknown; weights of the empty airplane, the fuel and cargo are already available with high precision. Passenger weight is on the order of 25-30% of the airplane's total weight.
Weighing the fully loaded airplane pre-takeoff, assuming a 2% accuracy, is therefore about equally accurate as obtaining the passenger weight with about 7% accuracy. Evidently the present system works well enough so that the proposed airplane scales would not be a cost effective improvement.
This is really amazingly retrograde thinking. Modern electronics with accurate load cells could easily establish the REAL take-off weight. Any deviation from the load sheet could then be quickly investigated. Correcting for lift in wind isn't an insuperable problem.