"The Ugliest Weenie" references CATS by Andrew Lloyd Webber, sharing almost the same plot in the musical. (In CATS, Grizabella is seen as an evil cat, before she gets their sympathy and goes to "The heavy SideLayer" either by climbing up a stair or on a platform. Just like in "The Ugliest Weenier" were The Ugliest Weenie is seen as a bad Weenie until it wins their sympathy and is dragged upwards.