The only free and comprehensive online etymological dictionary of the Spanish language
más, mas (Adverb, Conjunction) "more;" "but"

10th cent. Old Spanish maes. From Vulgar Latin *ma(g)is "there is more" or "yet." From Latin magis "more." From Proto-Italic *magis 'id.' From Proto-Indo-European *mǵ-i̯s "greater." From the root *meǵ- "great." See also mayor.

Romance: Western Vulgar Latin: ASturian más, Portuguese mais, Galician máis, Catalan més, French mais, Italian mai ; Eastern Vulgar Latin: Aromanian ma, Romanian mai ; Sardinian: mai

Italic: Oscan mais "more"

Indo-European: Celtic: Gaulish Magios (name) "great," Middle Irish maige "large;" Gothic: Gothic mikils "large," Old Norse mikill 'id.,' Old High German mihhil 'id.,' Old Saxon mikil 'id.,' Old English micel 'id.' (Middle English muchel, English much); Albanian: madh "large;" Hellenic: Ancient Greek μέγας (mégas) "large;" Armenian: mec "large;" Indo-Iranian: Sanskrit máhi- "large," Avestan mazōi "big;" Tocharian: A māk "many," B māka 'id.;' Anatolian: Hittite mekk- "much," Cuneiform Luwian maia- "many"
matar (Verb) "to kill"

10th cent. Of unknown origin. There are three plausible theories. The youngest theory is an origin in Arabic mata "he has died." The oldest theory is that matar derives from Latin mactare "to slaughter" through a hypothetical Vulgar Latin word *mattare. A final theory connects it to Latin mattus "stupified" via a Vulgar Latin word also reconstructed as *mattare. See Dworkin (2012) for a full discussion.

Romance: Western Vulgar Latin: Asturian matar, Portuguese matar, Galician matar, Catalan matar, Italian mattare

"Primary verbs of Arabic origin are rare in Spanish: achacar 'to blame, criticize', atamar 'to finish', halagar 'to flatter', recamar 'to embroider' atracar 'to bring a ship alongside the dock', zahorar 'to eat late, have a feast'. The verb nicar 'to copulate' turns up once in the Cancionero de Baena... Does the infrequency in the recipient language of primary verbs borrowed from Arabic constitute sufficient grounds to definitively reject the proposed Arabic etymology of Sp./Ptg. matar 'to kill'?" ~ S. Dworkin, A History of the Spanish Lexicon (2012)
matrimonio m. (Noun) "matrimony"

14th cent. Borrowed from Latin matrimonium 'id.' Literally a "mother-obligation." From matr- "mother" (see madre) and -monium "obligation" (see -monio).

Romance: Western Vulgar Latin: Portuguese matrimónio, Catalan matrimoni, Italian matrimonio; Eastern Vulgar Latin: Romanian matrimoniu

"“Marriage” has no Indo-European term. In speaking of the man it is simply said—and this in expressions which have often been remodeled in particular languages—that he “leads” (home) a woman whom another man has “given” him (Lat. uxorem ducere and nuptum dare; in speaking of the woman, that she enters into the “married state,” receiving a function rather than accomplishing an act (Lat. ire in matrimonium)." ~ E. Benveniste, Indo-European Language and Society (1973)

"No single term for 'marriage' can be reconstructed; different legal kinds of marriage were recognized, including marriage by abduction... In the daughter languages, 'to marry' (a woman) is usually expressed by a verb meaning 'to lead away' or 'to take' (as Latin uxorem ducere 'lead a wife, marry'), and this can be confidently projected back onto the proto-language." ~ B. Fortson, Indo-European Language and Culture (2011)
mayor (Adjective) "larger," "older"

12th cent. From Latin maior 'id.' From Proto-Italic *mag-jo- "greater." From Proto-Indo-European *mǵ-i̯ó- 'id.' From *meǵ- "great." See also más.

As for the origin of the surname: the Mayor was the master of a farmhouse or estate, thus called during the Medieval period.

Romance: Western Vulgar Latin: Asturian mayor, Portuguese maior, Galician maior, Catalan major, French majeur, maire, Italian maggiore; Eastern Vulgar Latin: Romanian maior ; Sardinian: magiori

Indo-European: Celtic: Gaulish Magios (name) "great," Middle Irish maige "large;" Gothic: Gothic mikils "large," Old Norse mikill 'id.,' Old High German mihhil 'id.,' Old Saxon mikil 'id.,' Old English micel 'id.' (Middle English muchel, English much); Albanian: madh "large;" Hellenic: Ancient Greek μέγας (mégas) "large;" Armenian: mec "large;" Indo-Iranian: Sanskrit máhi- "large," Avestan mazōi "big;" Tocharian: A māk "many," B māka 'id.;' Anatolian: Hittite mekk- "much," Cuneiform Luwian maia- "many"
me (Pronoun) "me"

From Latin me 'id.' From Proto-Italic *, me (unstressed). From Proto-Indo-European *h1me 'id.'

Romance: Western Vulgar Latin: Portuguese me, Galician me, French me, Italian mi ; Eastern Vulgar Latin: Aromanian mi, Romanian
media f. (Noun) "average;" "half of an hour"

17th cent. From Latin media "middle." From Proto-Italic *meþiā 'id.' From Proto-Indo-European *medhi̯-eh2- 'id.' From an archaic stem *me- "middle." See also medio.

Italic: Oscan mefiaí "on the middle," South Picene mefiín 'id.'

Indo-European: Celtic: Gaulish medio- "mid-," Old Irish mid- 'id.,' Germanic: Gothic midjis "middle," Old Norse miðr 'id.,' Old High German mitti 'id.' Old Saxon middi, Old English midde 'id.' (English mid-); Balto-Slavic: Old Church Slavonic meždaxъ "alleys," Russian mežá "boundary," Czech meze 'id.,' Polish miedza "border," Slovene méja "grove," Old Prussian median "wood," Lithuanian mẽdžias "forest," Latvian mežs "wood;" Hellenic: Ancient Greek μέσος (mésos) "middle;" Armenian: mēǰ "middle;" Indo-Iranian: Sanskrit mádhya- "middle," Old Avestan maidiia- 'id.'
mediar (Verb) "to mediate;" "to be in the middle"

From Latin mediare "to halve," "to divide." A verb formed from medius "middle" (see medio).

Romance: Western Vulgar Latin: Portuguese mear, French moyer, Italian mediare; Eastern Vulgar Latin: Romanian media
medicina f. (Noun) "medicine"

13th cent. Old Spanish melezina. From Latin medicina 'id.,' derived from medicus "healing" (see médico).

Romance: Western Vulgar Latin: Portuguese medicina, Galician medicina, French médecine, Italian medicina; Eastern Vulgar Latin: Romanian medicină
médico (Noun, Adjective) "doctor;" "medical"

Late 15th cent. From Latin medicus 'id.,' from mederi "to heal." From Proto-Italic *med-ē- "to heal," but originally "to measure healing." From Proto-Indo-European *med- "to measure."

In Spain, the title médica is considered disrespectful toward women and doctora is used in its stead.

Romance: Western Vulgar Latin: Asturian médicu, Portuguese médico, Catalan metge, Italian medico; Eastern Vulgar Latin: Aromanian medicu, Romanian medic; Sardinian: medicu

Indo-European: Celtic: Old Irish midithir "to measure," Middle Welsh meðu "to think," meddu "rule," Middle Cornish medhes "to say;" Germanic: Gothic mitan "to measure," Old Norse meta "to evaluate," Old High German mezzan "to measure," Old English metan 'id.' (English to measure); Hellenic: Ancient Greek μέδομαι (médomai) "to care for;" Armenian: mit-kʿ "mind;" Indo-Iranian: Young Avestan vī-māδaiiaṇta "they must measure"
medio m. (Noun, Adjective) "half;" "average;" "environment;" "middle"

12th cent. restoration from Latin medius "middle." The native word in Old Spanish was meyo but was replaced during the Middle Ages. From Proto-Italic *meþio 'id.' From Proto-Indo-European *medhi̯-o- 'id.' From an archaic stem *me- "middle." See also media.

Romance: Western Vulgar Latin: Asturian mediu, Portuguese médio, Catalan mig, French mi-, Italian medio; Eastern Vulgar Latin:njedz, Romanian mediu; Sardinian: mesu

Indo-European: Celtic: Gaulish medio- "mid-," Old Irish mid- 'id.,' Germanic: Gothic midjis "middle," Old Norse miðr 'id.,' Old High German mitti 'id.' Old Saxon middi, Old English midde 'id.' (English mid-); Balto-Slavic: Old Church Slavonic meždaxъ "alleys," Russian mežá "boundary," Czech meze 'id.,' Polish miedza "border," Slovene méja "grove," Old Prussian median "wood," Lithuanian mẽdžias "forest," Latvian mežs "wood;" Hellenic: Ancient Greek μέσος (mésos) "middle;" Armenian: mēǰ "middle;" Indo-Iranian: Sanskrit mádhya- "middle," Old Avestan maidiia- 'id.'