Just going by what he told us. There seems to be no reason for her to get fatter. She doesn't care about doing something about it (or is uncomfortable with that as the post says).
Yes, unconditional love is good. If my girlfriend or wife got fat, it doesn't mean I'd instantly leave her. However, I'd talk to her about it, find the exact cause. If she gets fat simply because she eats too much and doesn't care, yeah... I'd break up with her.
Is that because of what she looks like? No. There is way more than physical attraction or lack thereof. It is the personality trait of not caring for yourself and not caring for your relationship. A relationship requires effort throughout the whole relationship, not just the beginning.
I don't want to be with someone who changes like that after being nice and settled.