Eddie Cantor, not the first to use the song, frequently sang it in a melody with other songs, often just using the two choruses, leaving out parts of the verses by Clare and Conrad.

I think the version I posted in the Flirting Songs thread (link by Genie above) is the original from 1921, but I can't find reliable sheet music on the net. I have a typed copy, supposedly original, but without the original sheet music, I can't be sure.

It was first sung by Isham Jones and his Orchestra in 1922 and by the Benson Orchestra of Chicago in 1920-1921. Cantor make his hit versions in the 1930s. The Benson recordings have been re-issued on a CD collection, but I haven't heard them.
Many singers used the song, including Pearl Bailey, Count Basie, Bing Crosby, etc.

The Cantor versions all seem to be later than 1923, thus may be under copyright. He also used a longer title, "Ma, He's Making Eyes at Me."

Weaken' I believe is correct.