OK, we all know that epistemic modals such as may and might can be interchanged to express possibility in present & future
For example: he might be late, and he may be late are almost the same. Source
But might is also the past form of may in indirect speech:
For example: He said he might be late = He said "I may be late"
I had some feeling that people lived 100 or 200 or 300 years ago may have used may and might differently from what we are using nowadays.
I would guess, in the past, ‘he might be late’ means ‘it was possible that he is late’ and ‘he may be late’ means ‘it is possible that he is late’ The word might expresses it was possible and may expresses it is possible, but I may be wrong.
I found this information in this book "Grammatical Change in English World-Wide"
The book says:
"something might happen" in the past (maybe 1000 or 200 or longer time ago) (might + inf) is equivalent to "something might / may have happened" (might / may + have +PP) in Modern English.
Q: So, how were might and may used in the past?
Best Answer
"Might" was used somewhat more expansively in older English, as you can see from this search of the phrase "might have" in the King James Version of the Bible, first published in the year 1611:
https://www.blueletterbible.org/search/search.cfm?Criteria=%22might+have%22&t=KJV#s=s_primary_0_1