Older Briggs & Stratton engine with starter rope recoil issue

Here is a link to a video showing the issue:
 
This is an old tiller with a 5hp Briggs & Stratton engine. The starter mechanism started doing this recently. In short, after starting, the starter pull rope retracts / recoils correctly, but then will 'loosen' by a few inches, then retract again, over and over. 
 
I have replaced the starter rope, but I suspect most of the rest is original parts.
 
Any ideas what is causing this and how I can fix it?