Both "may" and "might" (the latter originally being the past tense or conditional of the former) have various distinct meanings in current English, cf. dictionaries.

When used to qualify statements like "You have heard", "may" gives it a probability between 20% and 90%, "might" would be between 5% and 20%, the remaining range being covered by "almost certainly" resp. "there is a faint chance" etc. Exact numbers of course vary.

However, given the English sense of irony, "might" is even used for absolute certainty in phrases like "You might prefer being late to being dead."

Ironic usage can modify many academic distinctions. For example: my English teacher told me that "ought to" could be used in lieu of "should" only when talking about a moral obligation. Well, how often do we encounter people saying "That ought to be sufficient", not realising they are being ironic.