I recall studies being done (80s? 90s?) on installing weighing machines on taxiways and/or aprons, but not the outcome.
This would be a much more cost effective way than having each aircraft weigh itself..it's not only the cost of installing the sensors etc in the aircraft. but the extra weight they crate, maintenance costs etc.
The difficulty was allowing for the different dimensions of different aircraft, as well as wind etc (previous posts) but they should not have been insuperable, I would have thought.