Yours, Etc.: Origins and Uses of 8 Sign-Offs
late 15c., "bellows for an organ," from wind (n.1) + bag (n.). Figurative sense of "person who talks too much" is attested from 1827.
A person who talks too much, esp a pompous prater; bag of wind, gasbag: a windbag who shoots the gab (1827+)