I learned You can use "may" to ask for permission or suggest something is possible. May I come in? It may rain today. And you use "might" to suggest a small possibility (smaller than "may") It might rain. I hope it helps you.

This is from the New York Times: ---- Distinguishing may and might can be tricky. The words have several meanings, which sometimes overlap, contributing to the confusion. ••• One sense of “may” is “be permitted to”: You may go now. In this sense it isn’t likely to be mixed up with “might,” though “can” is often used instead, especially in less formal contexts. ••• Trouble arises mainly when “may” and “might” convey possibility. Both words can carry this meaning, but there’s a difference in nuance. “May” simply states the possibility or likelihood, while “might” emphasizes the conditional nature of the possibility, introducing a greater level of uncertainty. He may go to the theater tonight (stating the possibility). He might go to the theater tonight (raising some doubt). ••• The same nuance arises in conditional constructions: If you are nice to him, he may help you out (the chances are good). If you are nice to him, he might help you out (but then again, maybe not). ••• With its greater sense of uncertainty, “might” is generally used in hypothetical and so-called contrary-to-fact expressions. If he were to come early, we might be able to finish the job (hypothetical). If you had been nice to him, he might have helped you out (contrary-to-fact). ••• And wait: there’s yet another source of confusion. Dictionaries also list “might” as the past tense of “may,” which seems puzzling since both words convey a present or future meaning. This past-tense function occurs in sequence-of-tense situations — a statement that originally uses “may” switches to “might” when it follows a past-tense verb: He may go to the theater. He said he might go to the theater.

May is more of a formal way of asking for permission or suggest something is possible. and Might is more of the informal way to ask for permission or suggest something is possible.