When I learned english, I learned that May is used for things that are possible and might for things that are less possible but still there's a small possibility, maybe the first one is like 60% and the other is like 40%. In the movie Pursuit of happiness, Will Smith tries to explain this to his son when talking about going to the Baseball game. Also might used for constructions in past as in "I might have given you the wrong answer" =)

"Might" is the past tense of "may". I might be late. I may be late. Both are correct. "Might" is also used to show less possibility of something happening than using "may" would. I might finish that assignment tonight, even though, I can't find my notes. I may finish that assignment tonight since I got so much done yesterday. Using "may" also shows you have permission. We asked last week and just found out we may use the car.

There is not much of a difference. You can use 'may' and 'might' as the same thing in most circumstances.