"May I go to the bathroom?" and "I asked if I might go to the bathroom."
The modal auxiliary 'may/might' is used to ask permission.
"He may not have understood your question." and "He might not have understood your question."
The same modal auxiliary is used for uncertainty.
Why?
According to OED 1, the oldest meaning (attested from the early 9th century) was “to be strong, have power or influence”—a sense still present in the noun might and the adjective mighty.
No later than the end of the 9th century the word was in use to express “objective possibility, opportunity, or absence of prohibitive conditions”.
The permissive sense developed somewhat later, around the year 1000: “To be allowed (to do something) by authority, rule, law, morality, reason, etc.”. This is a fairly obvious extension of the primary sense: to permit someone to do something is to grant them the “power” to do it.
What you describe as the “uncertainty” is attested by 1200. Again, it's a logical step: to say you are able to do something is different from saying you will do it, so may cedes ‘ability’ to can and assumes the sense of “Expressing subjective possibility, i.e. the admissibility of a supposition”.
Originally, might / may meant having the ability to do so. The noun might as in strength comes from the same root. This differed from the similar rôle of could / can in that originally might referred to power, could to knowledge.
From this origin, we have both the meanings you suggest.
That of uncertainty relates to possibility. It is true that I might have misread your question and be writing a useless answer, it is not true that I might grow wings and fly before I finish this sentence. I have the ability to do one, but not the other, but my saying I might do so does not mean that I will.
That of permission also relates to possibility; someone has the authority to permit or deny something (or perhaps in some circumstances we may cede them that authority before asking their leave, out of politeness), and hence it is they who we must ask if we may / might do something.
I'm afraid it's one of those features of the English language that you just have to accept without question or pause. Similarly, the modal "can" also has different functions (ability, permission). In fact, I'd say most, if not all, modals have many functions.
Etymologically, 'may/might' are linked to the idea of 'power', 'Macht' in German.
So asking for permission is ackowledging that someone has power over you.
That is why in our present world, which prides itself on having become more egalitarian than ever before, people prefer not to use 'may/might' when they are asking permission. It is felt as humbling – if not humiliating – oneself.
Instead, 'can/could', which come from the idea of 'know-how', 'kennen' in German, are used.
"Can I go to the bathroom?" is asking whether the objective conditions for my going to the bathroom are met… which is a bit blunt! The listener has been stripped of his or her authority almost entirely.
Putting 'can' in the conditional – "Could I go to the bathroom?" – does the trick of preserving both the speaker and the listener's dignity (*dignities?).
So, saying something 'may/might happen/have happened', dates back to a – religious – time when an ultimate authority granting or refusing permission for an event to happen was ackowledged: God's.
The uncertainty of the future was still felt as being to do with permission, hence the same modal auxiliary.
Se non è vero, (è ben trovato)!
