What would cause the outer edges of a two and a half year old's eye whites to become gray?

Blue sclera: What you are most likely noticing is something called blue sclera, in areas where the tough white connective tissue covering the eye (sclera) is thin enough to show the underlying vascular layer (choroid). This oftentimes can occur alone with no other issues, but it can also be found in certain rare connective tissue diseases. It's probably fine, but i would have a pediatrician take a look at it.