His name is a pun on 'stormy weather'; the literal as well as referring to dramatic personal situations that would require an attorney, perhaps also referring to fictional courtroom melodrama.
After Stan Marsh, Kyle Broflovski, Kenny McCormick , Clyde Donovan, and Jimmy Valmer watch the new Steven Spielberg and George Lucas movie, Indiana Jones and the Kingdom of the Crystal Skull, they decide to bring the movie directors to justice by hiring an attorney. The boys charge Steven Spielberg and George Lucas with "raping" Indiana Jones, and literally their childhood memories.
Stormy Weathers takes the case after the children plead and cry, reminding him that he felt the same way about the movie.
Taking the case to court, they win when everyone agrees that the latest Indiana Jones movie was a rape.
Stormy Weathers wears a blue suit consisting of blue pants, a blue coat, and a white shirt with a red tie. He has brown hair and brown eyebrows.