From bartley.com, When used to express permission, might has a higher degree of politeness than may. Thus, Might I express my opinion conveys less insistence than May I express my opinion.
According to the Guide to Grammar and Writing, Might is considerably more tentative than may,
May I leave class early?
If I've finished all my work and I'm really quiet, might I leave early?
politer or more polite, not more politer
Student or Learner