Why can't the undercarriage be fitted with sensors to "weigh" the aircraft?
Not really needed........
You have the basic empty weight of the aircraft ( from weight schedule)
Add the fuel, Crew, Pax, Pax baggage , Freight .Catering and potable water gives you the actual operating weight.
There is a system which uses a pressure sensor on the nose leg to verify the stab trim setting......ie the "green Band"