A patsy is a push-over, someone who can be easily manipulated by others. If your friend has convinced you that you should do all of his laundry out of the goodness of your heart, guess what? You're a patsy.
Patsy has its roots in 19th-century American slang, and it still has a slangy air to it. It may have started out as a character in an old vaudeville act named Patsy, who always got the blame when things went wrong. From there a patsy came to mean an easy target, someone who can be suckered into doing the bidding of more strong-willed people. If you show some backbone and assert yourself, you won't get the patsy treatment!