Green’s Dictionary of Slang

1. (US black) a braggart, a boaster; the quality of being one.

1926		Blind Lemon Jefferson ‘Dry Southern Blues’ 🎵 Take a trip down south and stop at a fatmouth’s house.
1929		M. Levin Reporter 22: Wish to thunder the god-damn fat-mouth would brain himself.
1942		D. Burley N.Y. Amsterdam Star-News 21 Nov. 16: Don’t let the [...] fat mouths jive you...Harlem is still Harlem.
1952		(con. 1948) G. Mandel Flee the Angry Strangers 80: Diane, overrelaxed, began to ramble and called herself a fatmouth.
1964		L. Hansberry Sign in Sidney Brustein’s Window in Three Negro Plays (1969) I ii: iris [to sydney]: Fat mouth.
1968		T. Wolfe Electric Kool-Aid Acid Test (1969) 165: You’ve got a fat mouth and you don’t know what to use it for! Ugly, that’s your trip.
1983		C. Heath A-Team 2 (1984) 166: Hey, fat mouth.
1984		LaBarge & Holt Sweetwater Gunslinger 201 (1990) 189: Sundance bristled. ‘How’d you like a couple of racetracks around your headlights, fat mouth?’.

2. a man who lets a woman, or women, take advantage of him.

1926		Blind Lemon Jefferson ‘Got the Blues’ 🎵 I was raised in Texas, schooled in Tennessee / I was raised in Texas, was schooled in Tennessee / Said woman, you can't make a fatmouth out of me.
1994		Calt I’d Rather Be the Devil 84: He was, at least by his own lights, far from being a ‘fatmouth’—a man who lavished money on females.

3. (US) verbosity.

1996

B. Woodward in Choice 5 Nov. 175: No, Hanson said, she suspected it was to give them fatmouth about the New York Times article.