AD620 In-Amp, single 5v supply, reference pin affecting gain
Notice the small block diagram in Fig.2 if the AD620 datasheet.



Here's a larger diagram from a datasheet of a similar InAmp with a 3-OpAmp topology (LT1920).



Notice that VREF is not a high impedance input.  In order not to skew the differential output stage, VREF should be connected to a low impedance output.  A voltage divider by itself is not a low impedance output.  However, the voltage divider can be buffered.



I have built and tested a similar circuit.  (In my case, the VREF came a source other than a potentiometer, though.)