Thing is, there is no technical reason that the aircraft weight cannot be determined automatically and cheaply. It really, *really*, is as easy as taking the bits out of three £10 set of domestic scales and glueing them on to the undercarriage legs.
Actually quite a few aircraft already have them installed as an optional extra but for economic reasons they were not very popular. It's not as simple as a £10 set of domestic scales and there were big reliability problems with the system of strain sensors. They can also be wildly inaccurate in different ambient conditions.
Assuming one doesn't fly out of places where baggage handlers would get bribed to overload aircraft, the system is not needed as it's just another cost.
Much like how CX and AA decided switched off their logo lights at night to save money, even if there are safety implications.