As the years pass, g sounds and y sounds tend to hop back and forth, changing places. Have you seen 'yett' for 'gate'? I have. And foryive for forgive?

I believe that may and might (which at one time would have had a gutteral sound at the end) were probably come from the same root, and there is no real difference between them.

I tried to do the right thing and look up the verb 'might' in my unabridged dictionary, and to my shock discovered that it's not there. I want my $1.00 back!

Well, they do offer one line of print which says that 'might' is the past tense of 'may'. How they figure that, I do not know.
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By the way, 'may' comes from the Anglo-Saxon 'maeg' meaning 'I am able to.' Sounds the same as 'I can,' doesn't it? I suspect the difference between 'can' and 'may' is something that someone thought OUGHT to exist. The distinction does make sense, but somehow it has never caught on.

I enjoy Joan Hess's novels of Arkansas, where people use nifty double constructions such as, "You might should call her and make sure she's all right."