For AD629, the output of the differential amplifier is not the exact difference of both the input. It is slightly higher.
For example: pin 3 = 2V, pin 2= 1V, pin 6 has to be 2V-1V=1V but observed is slightly greater than 1V (i.e. 1.2V or so - exact value not available). Thus it is not functioning as unity gain amplifier. Pl. help us to understand as to why we are seeing such a variation in output.
I am actually not seeing any problem on the attached schematic. I believe it also has the right output based on the figures that you provided.
With regards to your problem when your input is 2V and 1V, are you using the same setup as the attached schematic - Dual supply voltage of +/- 15V, both reference tied to ground, ground of the input voltage is common to the ground on the reference pin? Please refer below for the basic connection of the parts.