While elementary school teachers have done a thorough job of helping us all learn when to use may instead of can, the distinction between may and might isn’t quite so straightforward.
As academic editing service Enago explains, the main difference relates to how likely it is that whatever you’re talking about will come to pass. In general, statements with may indicate higher probability than those with might. If you tell someone that you may rewatch The Sopranos, you’re confessing that there’s a pretty good chance you’ll end up doing it—a better chance than if you were to say “I might rewatch The Sopranos.”
However, there are plenty of exceptions. For one, might is the past tense of may, so you should technically never use may if your statement is taking place in the past. “I predicted that he may rewatch The Sopranos,” for example, is incorrect; what you should have predicted was that he might rewatch The Sopranos. In those cases, whoever you’re talking to would just have to infer the degree of probability.
Furthermore, since may sometimes implies permission—which explains why teachers are often rigid about making students ask “May I go to the restroom?” rather than “Can I go to the restroom?”—it can get confusing when you’re not talking about permission at all. “I may rewatch The Sopranos” could hypothetically mean that someone has given you permission to use their HBO Now account to do just that. (If rewatching The Sopranos is sounding more and more appealing with every example in this article, you should know that HBO is currently offering that series and tons of other content for free, no subscription necessary.)
According to Writer’s Digest, grammar reference book Garner’s Modern American Usage considers it incorrect to use may with negative hypotheticals at all, because it’s especially easy to misinterpret them as situations where someone’s been forbidden from doing something. For instance, if you say “Kevin may not rewatch The Sopranos,” it sounds like you’re reporting that Kevin isn’t allowed to do so. “Kevin might not rewatch The Sopranos,” on the other hand, leaves much less room for confusion.
In short, you should stick with may if you’re talking about something in the present that is likely to happen, and go with might if you’re talking about something improbable, something in the past, or something paired with negatives like not or never.