arm (n.1)
"upper limb," Old English earm "arm," from Proto-Germanic *armaz (cognates: Old Saxon, Danish, Swedish, Middle Dutch, German arm, Old Norse armr, Old Frisian erm), from PIE root *ar- "fit, join" (cognates: Sanskrit irmah "arm," Armenian armukn "elbow," Old Prussian irmo "arm," Greek arthron "a joint," Latin armus "shoulder"). Arm of the sea was in Old English. Arm-twister "powerful persuader" is from 1938. Arm-wrestling is from 1899.
They wenten arme in arme yfere Into the gardyn [Chaucer]
arm (n.2)
"weapon," c.1300, armes (plural) "weapons of a warrior," from Old French armes (plural), "arms, war, warfare," mid-13c., from Latin arma "weapons" (including armor), literally "tools, implements (of war)," from PIE root *ar- "fit, join" (see arm (n.1)). The notion seems to be "that which is fitted together." Meaning "heraldic insignia" (in coat of arms, etc.) is early 14c.; originally they were borne on shields of fully armed knights or barons.
arm (v.)
"to furnish with weapons," c.1200, from Old French armer or directly from Latin armare, from arma (see arm (n.2)). Related: Armed; arming.