May has more than one definition. One of the definitions for May is the same as Might: He may throw a strike = he might throw a strike. (It is possible, but not certain). Another meaning of may is "to have permission": You may enter the house, but your dog may not. Please leave him outside. Might does not have this meaning. Of course, Might has another meaning as a noun: He had to use all his might (strength) to push the car up the hill.

Might is used for reproach, e.g. You might have done it.

might < may