It seems odd that the Brother of Lord Thomas Stanley would swap sides so soon after the beginning of Henry VII's reign. I want to ascertain the political, social or economic motivations that could have affected his decision to side with the supposed imposter, rather than support the King he helped usurp the throne in the first place.
William Stanley did not support Warbeck. In fact, he helped put the king on the throne and strongly supported him. Henry had Stanley set up by being falsely accused by a stool pigeon named Robert Clifford who was put up to it by Henry's men. Henry disliked that Stanley was very popular with everyone, and moreover he looked forward to seizing Stanley's estates which were considerable.
In short, Stanley was framed and killed for his money and to eliminate him as a possible rival to the king. The whole story can be found in "Memoirs of the rival houses of York and Lancaster" (1827) by Emma Roberts.