[rationalist]

Wouldn't it be possible to install strain gauges in the landing gears to determine the plane's weight?

[ooterness]

Systems built into the landing gear do exist, but they're not very common. There are also ground-based systems (i.e., scale-on-a-cart for each wheel).

https://aviation.stackexchange.com/questions/16307/how-does-...

[tadfisher]

They would have to be calibrated and cross-checked with the manifest weight

[Markoff]

seems it would be easier just to have them at boarding gate for all passing passengers