c. 1500, "beggar's child" ("... wyle beggar with thy brattis ...), originally slang, from a northern, Midlands and western England dialect word for "makeshift or ragged garment;" probably the same word as Old English bratt "cloak," which is from a Celtic source (compare Old Irish bratt "cloak, cloth"). The transferred meaning is perhaps from notion of "child's apron." Hollywood Brat Pack (modeled on 1950s Rat Pack) is from 1985. Brattery "nursery" is attested from 1788.
adjective suffix, "full of or characterized by," from Old English -ig, from Proto-Germanic *-iga- (source also of Dutch, Danish, German -ig, Gothic -egs), from PIE -(i)ko-, adjectival suffix, cognate with elements in Greek -ikos, Latin -icus (see -ic). Originally added to nouns in Old English; used from 13c. with verbs, and by 15c. even with other adjectives (for example crispy).
Others are reading
Definitions of bratty from WordNet
(used of an ill-mannered child) impolitely unruly;