The origin is unknown except that it was the work of David. However, here is a midpoint in its development:
David called her "chicky poo" in the first week, which my sister Juliana thought was "chicken poop." Um, no. Not.
And from there it became boo, and then The Boo. Boo has no relation to Boo Radley, yet I can't help but think of that name all the time.