My first reply here,
The MD-11 is fitted with just such a system, comprised of strain gauges on each axle which feed data to two weight and balance computers.
The calculated a/c weight is compared with the loadsheet prior to dispatch.
The system is also used as an alerting system in the event of possible a/c tip-over during loading.
The alert is triggered by the load on the nosewheels decreasing below a set value.
Once triggered it also cuts power to the cargo loading systems.
Works fine, as long as the housing for the strain gauges is kept perfectly sealed from any fluid leakage and carbon dust from the brakes.