Try switching the bridge connections to the + and - inputs round - then you output will increase with increasing load.
You probably might then need a balancing circuit to trim the zero reading to something around 0.4V or so (at low range of INA125's output, but not saturated).
If the circuit is sensitive to your hand it likely to be oscillating - you need a ground-plane for high-gain amp circuits like this and keep inputs shielded and away from outputs.