Belly-Up is a fish and seafood processing plant in Liberty City circa 2001. They use Mule trucks/vans (specifically, Triad Fish Vans) that are seen driving around Portland in Grand Theft Auto III. The name "belly up", as well as the logo, is a take on dead fish.
Crates bearing the Belly-Up logo can be seen at the docks in East Hook, Broker, Liberty City in Grand Theft Auto IV. They can easily be found right across the street from Brucie's Executive Auto Garage.