There have been some accidents due to wrong weight calculations that ended in fatalities, both in comercial and private aviation.
Besides this, though it is a simple task on the pilot's flight check list, it is a task. So I wonder, why don't aircraft have a built-in scale that would solve this problem and accurately give the total weight of the aircraft so it is safer and also one less item the pilot has to do.
(Aircraft scale source)
Instead of using a balance like the image above, it could be something installed inside the landing gear shock strut/cylinder that depending on the bar level it could tell the weight of the aircraft.
(source)