*The uses of 'May':
1-Permission:
May is more formal than can or could.It indicates respect for others:
EX:May I use your pen? To the police officer.
EX:Could I use your pen ? To a stranger.
EX:Can I use your pen? To a friend.
2-Weak possibility:(Deduction)
EX:It may snow tomorrow.It's weak because I haven't listened to the weather report but the air is cold and the sky looks the way it always looks before it snows.
EX:John may be sick.(He didn't tell me but his eyes look strange.
*The uses of 'Might' :
1-Weak possibility:
-In this use ,might is the same as 'may' although many grammarians believe that 'might' expresses a weaker possibility than 'may'
EX:It might snow tomorrow.(but probably won't)
EX:John might be sick.(but probably isn't)
Note: May/might +have +p.p. express weak possibility in the past (weak deduction)
EX:He may/might have gone to the club.I went home but he wasn't there .He didn't tell me that he went to the club but I think because he likes going to the club.
Note:If you want to express possibility,put in your mind that 'could' is stronger than may or might.
EX:We could have a vocabulary quiz tomorrow.We have just finished the lesson,and we usually have a quiz after each lesson.
EX:We might/may have a vocabulary quiz but I don't think we will.