Green’s Dictionary of Slang

(US) the process of gaining weight or the state of being fat.

1977		C. McFadden Serial 82: I wish I could eat stuff like that. I just have to look at it, you know? . . . Fat City.
1989		C. Hiaasen Skin Tight 279: He grabbed a gloveful of Reynaldo Flemm’s belly roll [...] Paydirt. Fat city.
1995		L. Stavsky et al. A2Z 20/2: Man, this club is fat city.
2005		WCBS 880 17 Feb. 🌐 While there may be nothing funny about fat, the dieters call Fat City the ‘Lourdes of Lard.’ But the city is better known as Durham, NC.