A few comments about weighing an airplane.
One issue is to be sure the airplane is levelled. Conceivably, that requirement may be relaxed if the only objective is to find out the total weight and the balance aspect (C of G) can be disregarded.
A second and maybe more problematic issue is that any wind affecting the airplane may introduce errors in the measurement. Wings produce lift, even at low airspeed. If the airplane happens to be parked head on to a breeze, the lifting force may be significant - and also dependent on the deck angle the airplane is sitting at. For this reason a proper weight & balance procedure (for GA aircraft anyway) takes place inside a hangar.
I don't know if these are real issues for transport airplanes in practical life, but they may be an additional reason why using estimated average passenger weights has been found a satisfactory method.
