"principal officer of a municipality, chief magistrate of a city or borough," c. 1300, mair, meir (mid-13c. as a surname), from Old French maire "head of a city or town government" (13c.), originally "greater, superior" (adj.), from Latin maior, major, comparative of magnus "great, large, big" (of size), "abundant" (of quantity), "great, considerable" (of value), "strong, powerful" (of force); of persons, "elder, aged," also, figuratively, "great, mighty, grand, important," from PIE *mag-no-, from root *meg- "great."
Mayoress is attested from late 15c. as "the wife of a mayor;" by 1863 as "woman holding the office of mayor."
It forms all or part of: acromegaly; Almagest; Charlemagne; maestro; magisterial; magistral; magistrate; Magna Carta; magnate; magnitude; magnum; magnanimity; magnanimous; magni-; Magnificat; magnificence; magnificent; magnify; magniloquence; magniloquent; Magnus; maharajah; maharishi; mahatma; Mahayana; Maia; majesty; major; major-domo; majority; majuscule; master; maxim; maximum; may (v.2) "to take part in May Day festivities;" May; mayor; mega-; megalo-; mickle; Mister; mistral; mistress; much; omega.
It is the hypothetical source of/evidence for its existence is provided by: Armenian mets "great;" Sanskrit mahat- "great, mazah- "greatness;" Avestan mazant- "great;" Hittite mekkish "great, large;" Greek megas "great, large;" Latin magnus "great, large, much, abundant," major "greater," maximus "greatest;" Middle Irish mag, maignech "great, large;" Middle Welsh meith "long, great."
also majordomo, "man employed to superintend a household, especially that of a sovereign or other dignitary," 1580s, via Italian maggiordomo or Spanish mayordomo, from Medieval Latin major domus "chief of the household," also "mayor of the palace" under the Merovingians, from Latin maior "greater" (see major (adj.)) + genitive of domus "house" (from PIE root *dem- "house, household").
1902, "enclosed automobile with open driver's seat," from French limousine, from Limousin, region in central France (see Limousine). The automobile meaning is from a perceived similarity of the car's profile to a type of hood worn by the inhabitants of that province. Since 1930s, it has been synonymous in American English with "luxury car." The word was applied from 1959 to vehicles that take people to and from large airports. Limousine liberal first attested 1969 (in reference to New York City Mayor John Lindsay).