opamp, ADC, level shift problem
Okay, so you want to use the 1.25V reference for the offset. This is basically the comment Scott Seidman made in schematic form: 







simulate this circuit &ndash; Schematic created using CircuitLab

The input common mode voltage is fine- it sits at 625mV fixed which is well within the range. Maximum input voltage is about 9mV peak. The op-amp output can't swing quite down to the negative rail with the load of the ADC input so you would get slightly more range by biasing it up by a smidge, but probably not enough to be worth bothering with given the large Vos uncertainty of that particular op-amp.