Supersize indicates to sizably increase the amount or the extent of something.
The phrase was particularly used by McDonald's restaurants to upsize their French fries and soft drinks to an extra-large size. In the United States, McDonald's began to phase out the supersized option from their regular menu in March 2004. The company stated the need to simplify their menu and to offer healthier food choices.
References
Supersize Wikipedia(Text) CC BY-SA