Measuring very small changes in resistor network using current source
Try this idea: -


5mA is generated by X1 and X5 - you'll need a stable voltage source where X6 is - it's referenced to the +5V to make life easier. If you are happy with your 5V rail stability it can just be a potential divider instead of the precision zener and R6 shown. X5 (AD8628) I used on a recent job but any 5V op-amp with decent offset voltage and inputs/outputs capable of getting near either rail will work. There are Plenty of P channel FETs that will do the job too - i picked this one because it has low Vgs(threshold) and there would be no-doubt it would work across the loads and power rails.

The AD627 is fairly standard and, for every ohm that R4 changes, the output (V out) alters 394 mV. The output offset is 2.5V (with a perfectly balanced bridge) but it could be set to 1V or if you had split supplies, 0V. Good luck.