What does Big Sleezy mean? May 21, 2017 All Dictionary Big Sleezy meaning in Urban Dictionary 1.)Pulling a sneaky maneuver where you would be the primary beneficiary2.) A rap team that has produced a number of no. 1 strikes including "Donovan" and "Whoawhoawhoa". Journey worldwide but by 3/22/10 the team is on "indefinite hiatus"