“Bigger snacks mean bigger slacks” is a one-line dieting saying that has been printed on many images. “Bigger snacks make bigger slacks” was printed in a 1982 newspaper. “Bigger snacks equal bigger slacks” was printed in a 1994 newspaper.
 
“Bigger snacks mean bigger slacks” has been cited in print since at least 2001. Authorship is unknown.
 
     
3 January 1982, The Tennessean (Nashville, TN), “Riverside Programs Can Put…,” pg. 10-E, col. 4:
DURING THE first week, all snacks are eliminated—“Bigger snacks make bigger slacks,” Rucker said. 
(Christine Rucker, Riverside’s community health educator.—ed.)
 
3 October 1984, Orlando (FL) Sentinel, “Program aims to shape up whole person” by Daniel D, Porter, pg. E6, col. 2:
TO help beat bad health habits, participants will be taught slogans, such as: “Bigger snacks make bigger slacks.”
 
25 December 1994, The Courier-Journal (Louisville, KY), “The Funnybone,” pg. H7, col. 3:
Bigger snacks equal bigger slacks.
—Joyce Mattingly, Eddyville, Ky.
 
Google Books
The Fattest Book of Fat Quotes (Ever)?
Edited by A. T. Jones
2001
Pg. ?:
“Bigger snacks mean bigger slacks.”
Unknown
 
22 September 2003, The Post-Standard (Syracuse, NY), “Losing weight pays off in upstate nurses’ diet challenge” by Amber Smith, pg. D1:
...line, such as: “Bigger snacks mean bigger slacks.”
 
9 January 2004, The Star Press (Muncie, IN), “Pluggers” (comic strip), pg. 6C, col. 4:
Pluggers know bigger snacks mean bigger slacks.
 
Google Books
Lullabies & Alibis: a novel
By Stephanie D. Lewis
Xlibris Corporation (Xlibris.com)
2008
Pg. 72:
And my well-meaning mother won’t say, “Bigger snacks mean bigger slacks.”
 
Twitter
Christie‏
@daxazo
Bigger snacks mean bigger slacks.
6:23 PM - 17 Mar 2008
 
Twitter
Joanna Sutter‏
@JoannaSutter
Bigger snacks mean bigger slacks.
5:02 PM - 27 Apr 2009
 
Twitter
Becca Horner‏
@beccahorner
Sign hanging on someones desk in the office: “Bigger snacks mean bigger slacks.” That is my new workout motivation motto.
12:48 PM - 15 May 2009
   
Odyssey
Body Image And The Mass Media
At Caldwell University
Jul 25, 2016
(...)
Catchy slogans like “A mind is a terrible thing to waste and a waist is a terrible thing to mind; A moment on the lips, a lifetime on the hips; Bigger snacks, bigger slacks; Burn calories not gas, and Commit to be fit” (32 Catchy Weight Loss Slogans and Taglines) convince people to become thin and muscular.