hi,
Assume a L/C excitation voltage of 10Vdc and L/C bridge sensitivity of 3mV/V
Also the mass being weighed is 200kG.
The L/C bridge would give an output of 3mV * 10Vext = 30mV at FSD of 200kG on the two Signal V1 ,V2 wires from the bridge.
Say you required an amplified voltage output of 5V, the amp would require a Gain of Vout/30mV = 166.67'
Choose R2 as 20k, this means that R1 would have to be in the order of 120R.
Plugging these values into the Vout = (V1-V2) * ( 1+ (R2/R1)) .
Vout = 0.03 * (1 + (20,000/120)) = +5.03V
E
EDIT:
This LTSpice sim shows your project.
It is IMPORTANT that the resistors are close tolerance, ideally 0.01%