1530s, "frothing, covered with barm;" see barm + -y (2). Figurative sense of "excited, flighty, bubbling with excitement" is from c. 1600. Meaning "foolish" (1892) is probably an alteration of balmy (q.v.).
barley
barleycorn
barm
barmaid
barman
barmy
barn
Barnabas
barnacle
Barnard
Barn-burner