I know that I am saying what has been said before, but I think a couple of points are worth repeating
1. It is not possible to explain clearly the differences between may and might.
For some people, may indicates a stronger possibility than might.
For others, the two words have the same meaning.
For others, particularly speakers of AmE, may does not exist. They use only might.
Many people do not realise that their way of using the word(s) may be different from others. That rarely, if ever, matters. If we know from context that the other person is not talking about permission, then whichever word they use, we know that they are talking about possibility. Such factors as context, the way the word may or might is stressed, facial expression, etc, may (!) suggest whether the speaker considers the situation referred to as a strong or weak possibility, but we have no guarantees.
2. The difference between could and might is not much clearer except when context tells us that could refers to ability. For me, could suggests some idea of circumstances permitting a possibility, might simply suggests the possibility:
Bill (Looking at a slightly fuzzy photograph of a group of people): Who's that person standing next to Mr Jones?
Ben: It could be my sister. (Ben knows that his sister was in the area at the time, and the person standing next to Mr Jones has long blonde hair, as does his sister.
Bill (Looking at a slightly fuzzy photograph of a group of people): Who's that person standing next to Mr Jones?
Ben: It might be my sister. (Ben is saying that it is possible that it is his sister. It is also possible that it is not.)
This difference becomes clearer if we negate the modals.
Bill: Isn't that your sister standing next to Mr Jones?
Ben: It couldn't be my sister. (Ben knows that his sister was in America when the photograph was taken)
Bill: Isn't that your sister standing next to Mr Jones?
Ben: It might not be my sister. (Ben is saying that it is possible that it is not his sister - but it is still possible that it is.)
I said that that was the difference for me. Others may see it differently.