This "Jokerized" episode was inspired by the Joker comic series which ran for nine issues from May, 1975 to October 1976. In those comics, Joker was the "hero" of the series, even though he was still a criminal. This story in particular borrows some elements from Joker #2 where Joker teams up with a criminal named Willie the Weeper, similar to The Weeper featured here.
Tim Conway portrays "The Weeper" who is a washed up older super villain. Conway was also known for portraying a washed up older superhero, Barnacle Boy in SpongeBob SquarePants (1999).
According to Batman, the Weeper's real name is Mortimer Gloom.