A popular “yo mama” insult “fat joke” is:
 
“Yo mama is so fat, when she sits around the house, she REALLY sits around the house.”
 
The joke has been cited in print since at least 1951, when it was a “bowlegged” joke—not a “fat” joke—that was told by one-line comedian Henny Youngman (1906-1998). The joke became a fat joke by the 1970s.
     
   
7 May 1951, Boston (MA) Daily Globe, “TV Diary” by R. F. McPartlin, pg. 16, col. 8:
Henny Youngman, on This Is Show Business: “I don’t say my wife is bow-legged, but when she sits around the house she sits around the house.”
 
4 December 1951, The Morning Herald (Uniontown, PA), “It Happened Last Night” by Earl Wilson, pg. 4, col. 2:
“So-and-So is so bowlegged,” she (Taffy Tuttle, a blonde Broadway showgirl—ed.) told me one night, “that when she sits around the house, she really sits around the house.”
 
Google News Archive
28 March 1962, Sarasota (FL) Journal, “It’s No Joke As Comic Try To Act Funny,” pg. 10, col. 6:
NEW YORK (AP)—“My girlfriend is so bowlegged,” said the young comedian, “that when she sits) around the house she REALLY sits around the house.”
 
30 October 1966, The Sunday Oregonian (Portland, OR), “My Favorite Jokes” by Billy Faldo, Parade magazine, pg. 14, col. 2:
I have a girl friend. She’s so skinny she looks like six o’clock up and down. She’s so bowlegged that when she sits around the house, she sits around the house.
   
Google Books
Encyclopedia of Humor
By Joey Adams
New York, NY: Bonanza Books
1968
Pg. 345:
My girl is so bowlegged, when she sits around the house — she sits around the house.
 
4 January 1979, Los Angeles (CA) Times, “Stage Review: Vallee at the Peak of His Form” by John C. Mahoney, pt. 4, pg. 14, col. 4:
For accelerated delivery, (Rudy—ed.) Vallee is without peer. he tells jokes. Like, “Are those your knees or are you smuggling walnuts?” and the immortal, “she’s so fat that when she sits around the house, she sits around the house.”
 
Google Books
Complete Book of Roasts, Boasts, and Toasts
By Elmer Pasta
West Nyack, NY: Parker Publishing Company
1982
Pg. 346:
She is so fat, when she sits around the house— she really sits around the house!
 
Google Books
A Prairie Home Companion
Pretty Good Joke Book (3rd edition)
By Brian Becker
Minneapolis, MN: HighBridge
2003
Pg. 75:
Yo’ mama is so fat, when she sits around the house, she sits around the housel
 
Google Books
Man Walks into a Bar:
Over 6,000 of the Most Hilarious Jokes, Funniest Insults and Gut-Busting One-Liners
By Stephen Arnott and Mike Haskins
Berkeley, CA: Ulysses Press
2007
Pg. 154:
Yo momma’s so fat, when she sits around the house, she really sits around the house.
 
Twitter
DeyNoFunny
‏@DeyNoFunny
Yo mamma’s so fat, when she sits around the house, she really sits A-R-O-U-N-D the house. #ABCDEFGHIJKLMNOPQRSTUVWXYZ
6:05 AM - 23 Jul 2016