May and Might

May has 2 uses in English:

 

1. Asking Politely for permission to do something:

This is used for people you do not know very well.

May I see the menu? / May I use your bathroom?

However, using may here is very formal in English, it is better to use could for polite questions:

Could I join you? / Could I take the afternoon off work next week?

 

2. Saying that something is possible

It may be sunny later but we have to wait and see / You may remember what I told you last week

Here it is also possible to use might or could for the same meaning.

It might be sunny later / it could be sunny later

To talk about things which possibly happened in the past we use may have:

Why is John late for the meeting? – He may have forgotten

                                                               - He may have got stuck in traffic

Might has just one use in English

1. Saying that something is possible:

This is used in exactly the same way as may above:

It might rain later / Remind me to show you that video because I might forget.

To talk about things that possibly happened in the past we use might have

Why is Steve so late for the party? He might have got lost on the way