Old English mæg "am able" (infinitive magan, past tense meahte, mihte), from Proto-Germanic root *mag-, infinitive *maganan (Old Frisian mei/muga/machte "have power, may;" Old Saxon mag/mugan/mahte; Middle Dutch mach/moghen/mohte; Dutch mag/mogen/mocht; Old High German mag/magan/mahta; German mag/mögen/mochte; Old Norse ma/mega/matte; Gothic mag/magan/mahte "to be able"), from PIE root *magh- "to be able, have power." A present-preterit verb (with can, shall, etc.). Also used in Old English as a "auxiliary of prediction."
"to celebrate May Day, to take part in May Day festivities," late 15c., from May. Maying as "the observance of May Day with all its sports and games" is attested from late 14c. (maiing).
And as a vapour, or a drop of raine
Once lost, can ne'r be found againe:
So when or you or I are made
A fable, song, or fleeting shade;
All love, all liking, all delight
Lies drown'd with us in endlesse night.
Then while time serves, and we are but decaying;
Come, my Corinna, come, let's goe a Maying.
[Robert Herrick, "Corinna's Going a-Maying," 1648]
"reckless, careless," 1828 (but suggested in other forms by 1793). As an oath or expression by 1815.
Old English mihte, meahte, originally the past tense of may (Old English magen "to be able"), thus "*may-ed." The noun might-have-been "something that might have happened but did not," also "someone that might have been greater but wasn't," is by 1848.
Old English agan (past tense ahte) "to have, to own," from Proto-Germanic *aiganan "to possess" (source also of Old Frisian aga "have to, ought to," Old Norse eiga, Old High German eigan, Gothic aigan "to possess, have"), from PIE root *aik- "be master of, possess."
The original sense is obsolete. The meaning "to have to repay, be indebted for" began in late Old English with the phrase agan to geldanne literally "to own to yield," which was used to translate Latin debere (earlier in Old English this would have been sceal "shall"); by late 12c. the phrase had been shortened to simply agan, and own (v.) took over this word's original sense.
The intransitive meaning "be in debt" is from mid-15c. To be owing to "be due or attributable to" is by 1650s.
also May-pole, "high striped pole decorated with flowers and ribbons for May Day merrymakers to dance around," attested from 1550s but certainly much older, as the first mention of it is in an ordinance banning them, and there are references to such erections, though not by this name, from a mid-14c. Welsh poem. See May Day.
It was usually cut and set up afresh on May-day morning, drawn by a long procession of oxen, decorated, as were also the pole itself and the wagon, with flowers and ribbons; but in some cases a pole once set up was left from year to year, as notably the famous pole of the parish of St. Andrew Undershaft in London, which was cut down in in reign of Edward VI. [Century Dictionary]