I think they hardly have some differense. Usually might means that you are little more unsure than when u use may but mostly they are told to be synonyms. And the other difference is that might is more common in everyday english rather than may which is more formal.
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khoshtipseems there is no difference between themYour observation is accurate. In effect there is no difference between them. At least not in the U.S. may is slightly more formal, but not by much. In everyday conversation, I almost always use might.
khoshtipI know the past tense ofthemay is might