LL2263-14 ADC input range question
From my understanding, the ADC should give a full scale reading if the
  differential input is 1.25V.


Not for this device.


  Also I'm actually using single ended input (grounding AIN- and feeding
  the signal at AIN+)


That would be incorrect - there are a few example circuits given in the data sheet that allow a single ended input to drive the two inputs differentially.


  I'm using 2V input range


A 2Vp-p differential signal is the limit; one of the differential signals is 1Vp-p and the other should be the same but inverted - net effect is a 2Vp-p differential signal.