For me, the "apple" doesn't relate to "eyes" but to "she". And "she" is only one person. So, she can only be "the apple" (one) of your eyes. She can't be "apples", that wouldn't work for a single person.

I was just reading - - the phrase originated in the King James version of the bible. I'm not sure that there is a reason it's only one eye. By the way the phrase apparently originally meant he pupil of the eye (I never knew that before).