Willow Weep for Me seems like one of those tunes that was in a musical or movie at some point, but that isn’t the case. Ann Ronnell wrote the tune, and it was first performed by two different groups, one led by Ted Fio Rito and another by Paul Whiteman, both in 1932. It hit the charts again in 1964 with the British pop group Chad and Jeremy. Some people have speculated that Gershwin wrote the tune and gave it to Ann Ronnell, but this has never been verified.
For the most part, we used the changes from the Hank Jones version (who generally used the Art Tatum version). It’s a little more complicated, but I really like these changes. I borrowed bar 5 (and other similar bars) from elsewhere.