Here's my analogy - if the person was drinking alcohol as much as they were eating, would it be a problem? If they were drinking to excess and unwilling to change, would you leave? If so, the eating addiction should be addressed - to be fair, you should clearly state your concerns - this behavior bothers me because - you are NOT asking them to change, you are outlining your boundaries around behavior. On the other hand, if the partner says: "hey, i know this got out of control, here's my plan to address it..." and then they do some things - well, perhaps give them credit and stick around. If they are unwilling to change, that's a sign of more problems to come, in my view.