A "Cheese Burger" is a drug reference, it is when the addict takes both an Upper or Meth-amphetamine such as speed or crank and mixes it with a Downer like morphine or Vicodin. It is usually taken while ingesting alcohol.
It creates a conflicting feeling in the body that most users love and become addicted to quickly.
The reference is attributed to a college fraternity (Theta Xi) from Edinboro University in Erie, PA. This became in the 1990's their "Offical" high of choice.