"Tighter than the skin on a grape” means very tight, such as someone tight with money or a tight sporting contest. “Tighter than the skin on a grape” has been cited in print since at least 1954. It’s not known who came up with the food expression.
By Robert Meyer
New York, NY: Washburn
Holidays It is important that visitors to Great Britain know the Bank Holidays there because on those days everything closes up tighter than the skin on a grape.
9 May 1954, Independent Press-Telegram (Long Beach, CA), “Wild Waves Are Saying” by Iola Masterson, pg. D-3, col. 2:
Sassy, our boys have that Junior Class sewed up tighter than the skin on a grape, don’t they?
19 February 1955, Los Angeles (CA) Times, “Cronin’s Corner” by Ned Cronin, pg. B3:
It was tighter than the skin on a grape.
19 April 1955, Los Angeles (CA) Times, “Cronin’s Corner” by Ned Cronin, pg. C3:
Bayer has this department locked up tighter than the skin on a grape.
Google News Archive
20 March 1964, Spokane (WA) Daily Chronicle/I>, “‘West Virginia ‘Bricktop’ Blows Out Roman Candle” by Robert C. Ruark, pg. 4, col. 8:
But she was business to the core, which is to say that in her club she was tighter than the skin on a grape.
By Ann Harleman
Ames, IA: University of Iowa Press
“Tighter than skin on a grape — that was my ex. Took me for everything I had.”
Circus of the Damned
By Laurell K. Hamilton
New York, NY: The Berkley Publishing Group
Jeans no tighter than the skin on a grape showed slender hips.