"long, loose outer garment," late 13c., from Old French robe "long, loose outer garment" (12c.), from a Germanic source (cf. Old High German rouba "vestments"), from West Germanic *raubo "booty" (cf. Old High German roub "robbery, breakage"), which also yielded rob (v.).
Presumably the notion is of garments taken from the enemy as spoils, and the Old French word had a secondary sense of "plunder, booty," while Germanic cognates had both senses; e.g. Old English reaf "plunder, booty, spoil; garment, armor, vestment." Meaning "dressing gown" is from 1854. Metonymic sense of "the legal profession" is attested from 1640s.