Richard Verber ranks up there. He was very obese.
"Richard William Verber was born on June 3, 1944 in Cleveland, Ohio. After moving to Chicago, he became a National Master in 1961, and a Senior Master in 1971. He won the 1962 Chicago Open and 1966 North Central Open, and tied for first in the 1970 Illinois Open. He represented the United States at the World Student Team Championships in 1967, 1969, and 1970. In the 1970 event in Haifa, Israel, his 5½-1½ score won the gold medal on fourth board, and helped the U.S. win the Championship. In 1974 and 1975, he declined invitations to play in the U.S. Closed Championship.
Verber was also a National Tournament Director, and organized many important events in Chicago, including multiple U.S. Opens, U.S. Championships, international title tournaments, and simultaneous exhibitions by the world's leading players. He died on December 10, 2001 from complications associated with obesity."
http://www.chessgames.com/perl/chessplayer?pid=101268
http://articles.chicagotribune.com/2001-12-16/news/0112160004_1_chess-master-chess-federation-chess-scholars
Serious question.
Recently I was tournament director for a "fat bald blokes" event on chess.com: https://www.chess.com/tournament/tournament-for-fat-bald-blokes
The idea for this question arose after reading and posting on a thread about performance. I'm reading a good book at the moment called "Grain Brain" about the effects of gluten on the body and especially the brain. To cut a long story short, the author states that big bellies are correlated with smaller(shrinking) brains. Chess being the art of analysis and our brains being our chess engines, so to speak.
I do notice that the best players are often quite thin and gangly but not always ! Hence the thread title....