O.E. mihte, meahte, originally the past tense of may (O.E. magen "to be able"), thus "*may-ed." See may (v.). The first record of might-have-been is from 1848.
O.E. miht, earlier mæht, from P.Gmc. *makhtuz (cf. O.N. mattr, O.Fris., M.Du. macht, Ger. Macht, Goth. mahts), from PIE base *mag- "be able, have power" (see may (v.)). Mighty (adj.) is from O.E. mihtig, earlier mæhtig, from miht. As an adverb, it is attested from c.1300, though now considered colloquial.