How to amplify a small AC (no DC offset) wave with an op-amp powered from a 0-5V rail and a pot-varying gain?
To 'sum' your AC wave with a 2.5V offset, simply couple the wave through a capacitor. This provides high pass filtering with a cutoff frequency determined by the capacitance and resistance at the junction. 

Similarly you can vary the AC gain of your amplifier (while the DC gain remains fixed) by AC coupling the feedback pot. Here is an example circuit:-     







simulate this circuit &ndash; Schematic created using CircuitLab

In this circuit R1 and R2 provide the 2.5V bias, and the AC waveform is mixed into it via C1. R3 couples the output of the op amp back into the inverting input to provide a DC gain of 1. R4 and R5 increase the AC gain to between ~+2 and +21 (205k/105k to 105k/5k) while C2 blocks the effect of R4 and R5 at DC.

With this feedback arrangement the pot is more sensitive at high gain, and the minimum gain is just under +2. There are other ways to connect the pot which can provide different adjustment ranges, eg. pot across R3, or one pot end to the output, pot wiper to the - input, and the other pot end to R5. In all cases the feedback path to ground must be coupled through a capacitor to avoid upsetting the DC gain and output offset.