INA126P gain is exactly double what it should be
If this is a DC signal, have you accounted for input offset voltages and input bias currents? 

Or does setting the input to 0V do you get 1.5mV? 

Given the data in the question, 0.6 mV in would either give you 4.5 mV (input offsets) or 6 mV (doubled gain) allowing you to distinguish between these possibilities.