coat of arms (n.)

early 14c., "principal outer garment, tunic, kirtle," typically made of cloth and usually with sleeves, worn alone or under a mantle, from Old French cote "coat, robe, tunic, overgarment," from Frankish *kotta "coarse cloth" or some other Germanic source (compare Old Saxon kot "woolen mantle," Old High German chozza "cloak of coarse wool," German Kotze "a coarse coat"); the ultimate origin is unknown.  Spanish, Portuguese cota, Italian cotta are Germanic loan-words.

Coats of modern form, fitted to the body and having loose skirts, first appeared in the reign of Charles II of England. Since the beginning of the eighteenth century the coat has been of two general fashions: a broad-skirted coat, now reduced to the form of the frock-coat ..., and a coat with the skirts cut away at the sides (the modern dress coat), worn now only as a part of what is called evening dress. [Century Dictionary, 1897]

As "garment worn suspended from the waist by women and children" from late 14c. (the sense in petticoat). Transferred late 14c. to "the natural external covering of an animal." Extended 1660s to "a thin layer of any substance covering any surface." Coat-hanger "clothes-hanger designed to facilitate the hanging of a coat" is from 1872. Coat-card (1560s) was any playing card which has a figure on it (compare face-card). It later was corrupted to court-card(1640s).

[weapon], c. 1300, armes (plural) "weapons of a warrior," from Old French armes (plural), "arms, weapons; war, warfare" (11c.), from Latin arma "weapons" (including armor), literally "tools, implements (of war)," from PIE *ar(ə)mo-, suffixed form of root *ar- "to fit together." The notion seems to be "that which is fitted together." Compare arm (n.1).

The meaning "branch of military service" is from 1798, hence "branch of any organization" (by 1952). The meaning "heraldic insignia" (in coat of arms, etc.) is early 14c., from a use in Old French; originally they were borne on shields of fully armed knights or barons. To be up in arms figuratively is from 1704; to bear arms "do military service" is by 1640s.

1550s, from turn (v.) + coat (n.). The image is of one who attempts to hide the badge of his party or leader. The expression to turn one's coat "change principles or party" is recorded from 1570s.