OK I think see now. Correct me if I'm wrong:
You have an amplifier that takes a differential signal from a load cell and outputs a single-ended signal to the A/D input. There is a minimum force on the load cell which is quite high. So the problem is that when you adjust the amplifier's gain to get enough resolution, the output voltage is (or may go, when even more force is added) outside the voltage range of the A/D input.
Assuming that's the case, then if the range of force is still within the acceptable range for the amplifier, then you can subtract some voltage from the single-ended signal that goes from the amp to the A/D input, which is pretty easy. You'd just need two resistors (as a voltage divider) and a negative power supply. Then account for the different gain and offset in the software.
However, if the output of the load cell is too much for the amplifier, then all I can say is you need another amplifier with a wider dynamic range. This is because if you try to make a simple voltage divider circuit with the signal from the load cell you are liable to cause nonlinear or indeterministic things to happen to that signal, because we don't know the circuitry driving that load cell output signal. If you try to avoid that problem by making a very high impedance voltage divider, then noise might become a problem or the amp's input impedance might start to make a difference. If you're going to make an op-amp preamp, then you might as well get rid of the main amplifier and just use the single-ended output of the op-amp to drive the A/D--and that's an OK solution as long as the op-amp ckt has the dynamic range you want and provides an offset.