A question about non-linearity of an in-amp gain

I'm observing nonlinearities in microvolt range inputs on an instrumentation amplifier. Here is the amplififer datasheet and its gain is supposed to be:

G = 1 + (49.4 kΩ/Rg)

And the inputs to this amplifier(from a strain-gage) will be in -/+2mV range in my case.

So I wanted to see the gain at different differential inputs in simulation.

Below the inputs to the amplifier are +/-1mV, so the differential input signal Vsig = (+Sig) -(-Sig) = 2mV and Vout = 1.6V. Here the gain is then around 780. Below is the plot for these:

And this time below the inputs to the amplifier are +/-1μV, so the Vsig = 0.2μV and Vout = -38mV. But this time the gain is around 190k(LTspice shows 19k). Below is the plot for this case:

To see this non-linearity I made a DC sweep for 0.1mV...2mV range and here is what I get:

Am I doing something wrong here? If not would this nonlinearity have bad results for my -/+2mV range strain-gage inputs to the amplifier.

Edit:

Common mode voltage added to the inputs as will exist in real scenario:

• AD8221 has up to 25 uV offset voltage. That alone will produce a nonlinear response, probably noticeable for input amplitudes below 100 uV. Apr 3, 2017 at 17:48
• @ThePhoton Does that mean for small strain changes there will be great error in measurements? What could be the workaround for these in electrical side besides using more sensitive gages? Apr 3, 2017 at 17:53
• What are your power supplies, and are you good with the allowed common mode input ranges? Apr 3, 2017 at 17:53
• Yes, that's close enough to what I meant. If you have solved your problem, be sure to post an answer explaining the solution. Apr 3, 2017 at 20:39
• @Enric Blanco This is my first answer. I also added some extra I would be glad if you agree my answer. Its not practical to tie the inputs all the time. Apr 3, 2017 at 21:12