In "I Should Have Never Gone Ziplining", Cartman was excessively drinking Mountain Dew, and its variants, in order to cope with the various tour groups. Combined with his stomach contents from his previous night's dinner, this gave him severe flatulence and later, severe diarrhea. The aforementioned diarrhea later attracted beavers, resulting in the boys having to fight them off.
Double Dew has twice the caffeine and sugar of regular Mountain Dew, which resulted in Cartman's diarrhea worsening significantly.
It can also be seen briefly in The Stick of Truth in the basement when you meet the Bard.
Diet Double Dew
Diet Double Dew contains half the caffeine and sugar of Double Dew, making it equivalent to a can of regular Mountain Dew. Cartman, not realizing this, claims that Diet Double Dew does not give him diarrhea.