1. Change to first person view;
2. Activate free view mode (double Alt);
3. Move head to the right more than 90 degrees;
4. Press right mouse button to move into weapon sight mode.

You will notice that:
a. Your head moves back to standard postion;
b. Go to weapon sight mode;
c. Weapon moves to the right till aiming deadzone limit (didn't return to postion on step 3).

I think that the right choice is to make:

1. You turn to the right;
2. You go to weapon sight mode.

Make them simultaneous or in steps: step 1 and then step 2.

Also fix the aiming deadzone. Zero point for it should be head postion but not torso.