Just now I was browsing the forum and was reminded of an old Flash game I played a couple times back then. Unfortunately I don’t remember its name, so I’m putting this out here in case it flips a switch on someone’s brain as well or encourages anyone to look alongside my own search.
Basically, the game had Angry Birds-style gameplay where you, as a fat guy/group of fat people, decided to enact revenge upon fast food chains for making people fat. You’d launch yourself from a catapult/cannon at a fast food restaurant, aiming to cause as much destruction as possible, and get money for it you could use to get more characters (most of which were pop culture references), get upgrades for your launcher or (ironically) fatten yourself up more.
As you can probably tell, the game had more of a comedic tone than a fetishy one (the main character even dies of a heart attack in the end), but I figured some people would still appreciate having one more weight gain game to play if I just could find this game in the Internet somewhere.
EDIT: Found it (thanks gamingcat02261991!), here is the .swf file if you have a projector you want to try it on: