You are nixing your own question by saying "except in cases of I'll health/mental health issues/etc etc"; you're basically only allowing for the case where an otherwise perfectly contented person decides to regularly consume excess calories for the merry hell of it. This is hardly anyone, and especially hardly any women. Women in western culture (and indeed in most cultures) have a fucked up relationship with food of one sort or another foisted on them almost as soon as they can talk. It is never just as simple as fancying a few extra biscuits too often if you're talking significant weight gain (4-5 st). Gaining that kind of weight (absent a physical cause) takes either a long time or extreme overeating, it hurts your joints, your clothes don't fit, it's expensive. Noone gets that way or stays that way because they simply can't be arsed to do anything about it. Its a compulsion. It's stress, exhaustion, depression, isolation, the feeling of having nothing for yourself except what comfort you can cram in at your desk or in the car between work and nursery and afterschool clubs, it's never just gluttony because there's always an unmet need underlying the decision to overeat.
My view is that overeating is alcoholism for people who can't afford for their life to spiral, people with others who depend on them to keep the wheels on - so basically women. If a woman who binge eats was a man, she'd be drinking 10 cans of cider, falling down drunk, throwing up on the living room and unable to get up the next morning from the hangover. A wife, a mother, a working woman usually cant do that, as no-one is going to pick up the pieces, get the kids to school, clear up the puke. So instead they eat a family size dairy milk and a grab bag of crisps with their single glass of wine, so the only person who suffers for their dysfunctional self-soothing mechanism is themselves.
Noone who puts on 4-5 stone in a couple of years is just glibly "choosing" that.
I have gone from around 10.5 stone to around 14 in the last 5 years and I sometimes feel amazed none of the people in my life are just appalled and worried and asking me if I'm ok. Because I'm not. I'm like this, and I'm overeating, not because it makes me happy. It's making me sick and uncomfortable and in pain. I'm doing it because I can't stop.
To answer your question, sudden excessive weight gain is a perfectly legit reason to leave your partner. But so is waking up in the morning, looking at them and just not liking their face any more. Anyone can legitimately leave any relationship for any reason. I think the quality of the overall relationship, and the commitments that depend on it (e.g. children) will determine how important physical appearance will be in deciding to call if a day or not. It's not a question of "is it a good enough reason for someone to leave someone?"; more "how important is this to you given the context?".
Certainly I can't see anyone suffering from overeating being motivated to stop it by the idea their partner will leave them if they don't. Indeed I can only imagine feeling as shit and anxious as that would make someone feel would only tighten the spiral of addictive behaviour.