What methods are used to achieve that?
According to my search :
- For old planes they use a plumb bob and measuring tools.
- On new and big planes, the process is computerized. Built-In Electronic Weighing like the Boeing 777
Having recently weighed my plane I can tell you what's involved for determining the Basic Empty Weight for a small aircraft:
As Terry mentioned, setting up took more time than the actual weighing and calculations. In my case I spent about a day straightening out the equipment list, and the shop that did the weighing spent about 20 minutes verifying that I hadn't missed anything. Defueling the aircraft adds a significant amount of time to the process as well. Moving the plane onto the scales and leveling it took approximately 15 minutes, and doing the math took maybe another 5 minutes.
On larger aircraft the same general process can be used with larger scales (or jacks) - load cells integrated into a taxiway or ramp area are another option for doing this.
I'm not sure if aircraft that can determine their operating weight (by load cells installed in the gear assembly) can also determine their own empty weight - I know the weighing report I received includes calibration information for the scales used, so presumably weighing a large aircraft using its built-in load cells would require those cells to be properly (traceably) calibrated prior to using them for this purpose.