May and Might both suggest uncertainty, but they offer different degree/perspective/perception. There might/may be situations where they can be interchangeable. (like this very sentence :-)) may and might - one suggests something that is less likely to happen and the other suggests something that is more likely to happen.
While might suggests possibility, may suggests probability.
Consider the following sentences -
The CEO might resign.
The CEO may resign.
In both sentences above the uncertainty about his resignation is looming. But there is a difference in register. Sentence #1, possibility and sentence #2, probability.
In sentence #2, the resignation is likely to happen, but not certain. In sentence #1, there are more chance of resignation, yet uncertain.
Even saying so, in both these sentences the difference is effectively very subtle.
OP's sentence -
You ____ (may/might) go now if you want to.
We need either may or might to feel that blank. That blank should contain a word that will suggest uncertainty.
If you use may, it's a plain statement of uncertainty. But if you use might, you are suggesting there is more chance of your going, though uncertain.
So both are possible depending on context.