The ADC is used to measure ac current, so, I shift the current signal to 1.65V when the real current is 0. It's just the mid ADC range. So I think what you said is right . But I don't know the background why MSB transition region will have the greate...

I have exactly the same problem. Did you solve it? In my case , the single ended input is provided around 1.65V. But it still works like your fig