Some of the information is Boop-Oop-a-Dooping full of SPOILERS. Boop-Oop-a-Doop!
"That's My Weakness Now" was written by Sam H. Stept and Bud Green (words and music) in 1928. This became their first hit song together, made popular by singer Helen Kane the same year. Betty Boop performs it in Stopping the Show (1932), the first cartoon in the actual Betty Boop series, which was a recreation of a vaudeville show in which Betty comes out on stage and performs some impersonations of celebrities. Each one of these are set up with a little photograph of the personality where they animated the lips, like Fanny Brice, who says "Can you imitate me, Betty Boop?" The very first one though is not set up that way. It begins with a long shot which pans over the audience, and in the background you can see the image that would be on the photograph, which looks like the silhouette of Helen Kane, yet it immediately cuts to Betty singing "That's My Weakness Now", the song that Kane made famous, yet there is no intro of Helen Kane to establish that she is the one being imitated. The clip was cut, as you can hear the splice and see the thing in the background. It was cut because of Kane's infringement lawsuit, where they showed the films at the court, to compare the Helen Kane films to the Betty Boop ones in order to see if any deliberate parallels could be found. Had that scene been left, Kane might have won the lawsuit she launched against Paramount Pictures and Fleischer Studios.