Calculating its total weight is one thing, but calculating the distribution of the weight is a different matter.
The aircraft sits on three legs. This is sufficient to be able to calculate the total weight and 2-axis C of G (which is all that is required). An electronic load cell is not expensive, and could be fitted to each landing strut (though would have to be done at the design stage, I doubt retro-fitting would be possible).
Alternatively the pressure of gas in the oleo would surely be proportional to the weight on that landing strut? A pressure sensor on each oleo could probably be retro-fitted.