Instrumentation Amplifier - how to use it correctly
Input voltage range issue.  With 0 &amp; +5 supplies, the input range is only 1 to 4 volts.  Your inputs are below the range where this amp will work.  Check "linear input range" on datasheet.

One fix is to get negative voltage on V-.  Another is to bias one end of the voltage measurement.  Eg, bias the low side to 1.5 V and leave the high side unbiased/high impedance.