AD620 In-Amp, single 5v supply, reference pin affecting gain

AD620 In-Amp, single 5v supply, reference pin affecting gain

Given the datasheet here, I can't explain my observations with my AD620 test circuit.
The circuit:
Supply: +5v / 0v (Well regulated)
1k potentiometer across the supply, with the wiper going to both the reference pin and the negative input
+ve/-ve inputs: K-type thermocouple. (41uV/K)
Gain resistor: 100 Ohm (Gain of 500).
It seems that the gain is strongly dependent on the voltage of the reference pin. If I set the pot at precisely 2.5v, I get roughly the expected gain. But even slighly higher or lower and the gain reduces significantly. (For example, just +/- 0.05V change in reference reduces gain by about 10% for output signals of +/- 100mV). I've been taking measurements with a standard multimeter.
I haven't done extensive testing with this, but none the less have lost a fair bit of hair. Is there something obviously wrong with what I'm doing? I must have run through the figures in the datasheet two dozen times. Is it the circuit at fault? Or my measurements? Or both?
Thanks