May and might are both used to talk about the chances of something happening and to ask for and give permission. They are mainly used to talk about the present and future. The difference between them is that might is used for less probable things and may for more probable:
I may go to London tomorrow (50% chance)
I might go to London tomorrow (30% chance)
Both are very formal and Might is more polite than May
Might/May I have a glass of water?
As May is stronger than Might permission is given with May.
Might/May I have a glass of water? Yes, you may. (not
Yes, you might)
If we want to talk about permission in the past we use could/be allowed to.
|possibility||It may rain today.||–|
|permission to do sth. in the present||May I sit here?||Am I allowed to sit here?|
|polite offer||May I help you?||–|
|possibility (less possible than may)||It might rain today.|
|permission to do sth. in the present||Might I sit here?|
|very polite offer||Might I help you?|