Might is the past tense of may (See can). Avoid such nonstandard expressions as "might of and "might could" (for might have or might). In the senses of possibility and permission, may is more intense than might."He may die" is stronger than "He might die," and "May I stay?" is more forceful than "Might I stay?" As a noun, might appears in such trite expressions as "with might and main" and "with all his might." Mighty is informal in the sense of "very" (mighty scared).
Dictionary of problem words and expressions. Harry Shaw. 1975.