when should we use may and when might?
"I might go"/"It might rain" both show a weaker level of certainty than "I may go"/"It may rain".
Because 'might' is weaker epistemically, it is also used, though it's not overly common, as a softer form of politeness, a deontic use.
Might I borrow a pen?
See the thread "Modals of Speculation" for a more complete discussion.