"It may be true" means a stronger possibility. "It might be true" means a weaker possibility. I consider "might" to be the weakest possibility of all the modals.

Most of the times, there is hardly any difference between ''may'' and ''might'', so either one you choose is fine. In other words, both of your examples are ok to use. However, sometimes there is a distinction between ''may have'' and ''might have''. I think this article is very enlightening on this matter. Check it out if you'd like: http://www.oxforddictionaries.com/words/may-or-might I hope that helped!

Both of your example sentences sound fine to me. In that way, they are interchangeable. There are different meanings where they aren't of course.

All of these answers are great! I agree with Peachey that generally speaking "may" has a stronger possibility and "might" has a weaker one. In this way, they're interchangeable to a point. "May" can be used in the same context of "might" past discussion of possibility. Both can be used to communicate permission. I.E. 1: May I go to the bathroom? 2: Yes, you may go to the bathroom. Less commonly, "might" is used. I.E. 1. Might I go to the bathroom? 2. Yes. (I've never heard someone reply with "Yes, you might.") Another important thing to note is "might" is used as a past tense of "may". I.E. If he says "I may be late to the party." His friend could tell the others "He said he might be late to the party." If you have any questions please contact me. :)