There’s additional resistance in your circuit that you are ignoring. This is in the wires and connectors. What you will want to do is to calibrate the system. Take two readings at known weights (ir in your case, whatever the bridge is measuring) and, assuming things are linear, apply a slope/intercept calibration curve (y=mx+b) to your readings. Any time you are measuring things in the real world, you need to either do your own calibration or take advantage of calibration provided by the manufacturer of the sensors.
/mike