Sweet William is a large burly member of Cat R. Waul's Cactus Cat Gang who appears as a minor antagonist in An American Tail : Fievel Goes West and reappearing as the secondary antagonist in Fievel's American Tails.
An American Tail: Fievel Goes West
Williams just appears as a background character, like most of the other members of the gang.
Fievel's American Tails
He plays bigger role in the show. In one episode, "Mail Order Mayhem", he plays out as the main bad guy, working with two other cats Slim and Felonius without Cat R. Waul's authority (as far as we know). In this episode he orders a "Mouse Slapper" which fires nets on mice, and he terrorizes the town with it, but is easily subdued by hired lawmouse Clint Mousewood. In another episode he reveals a soft side, taking a liking to Yasha Mousekewitz and finding her too adorable to eat when she wanders into his hideout in "Babysitting Blues". In "Bell the Cats" once again he is the main villain, with Waul being absent for unknown reasons, keeping the mice of Green River in the grip of fear until Fievel ties a bell on his tail and the tails of his gang.
It appears that after Waul was ousted from Green River at the end of Fievel Goes West, Sweet William no longer took orders from Waul unless there was something in it for him, and in fact beats Waul up in many episodes. Often times he causes more danger than Waul does, in the episodes where he's the main villain.