May and Might

'May' is used when we want to express a possibility. It shows that there is a possibility that something will happen or be true but this is not certain.

'May' is used when we want to politely ask permission for doing something. Using 'May I...?' is more polite than using 'Can I...?' or 'Could I...?'
The use of 'may' in this way is very formal and very polite.

If you want to politely give permission to somebody, you can also use 'may'.

You can use 'may not' or 'mayn't' (spoken) not to allow somebody to do something.

You can use 'may' to express wishes. In this function, you can only use 'may'. 'May' and 'might' are not interchangeable in this case.

We can use 'may' in spoken English and in formal situations to say, ask, or suggest something in a polite way:

'Might' is similar to the first function of 'may', which is expressing possibility. But the difference is that with 'might' the possibility is less likely. It is more remote, the chances are smaller.

We use 'might' as the past tense of 'may' when we want to report that someone talked or thought about the possibility of something:

We can also use 'might' to express a possibility in the past that did not actually happen.

Especially in British English, 'might' is used for politely asking permission to do something. But, it is very rare and very formal.

We can use 'might' to suggest politely what someone should do.

If you're not sure that something has happened in the past, it's better to use 'might'. You can use 'may', too, but since 'might' is the past tense of 'may', you can use 'might'.
After 'might' in this use, you should use a past perfect tense after your modals.