As far as I understand it, people who used to be born underdeveloped and that were called midgets, are now able to get treated medically, when young, so that they can grow to a more “normal” stature.
As I understand it the term ‘little people’ is preferred by many because they believe it is important to remind everyone that they are human (despite how they are sometimes treated) and that their height does not define who they are:
After writing that last post it also occurred to me that there is an untrue assumption in the OP, namely that the word midget has BECOME offensive. Given the poor treatment of little people throughout the ages, I suspect the word has never had a positive association and that it has never actually been used as a term of affection