Absolutely agreed that the correct course of action here involves communication, and that your wife sounds very depressed, but I kinda take issue with the idea that you were somehow complicit in her weight gain and depression. To my untrained eyes, this looks like severe chemical depression, which often results in weight gain, which feeds the depression further, as does the shit state of any relationships the person has as well. I've seen it before, and it's a very, very sad and difficult thing, but it can be treated - this involves hard work and medication, if in fact it's chemical, but again, I can't evaluate that, nor would I attempt to via proxy even if I were qualified to do so. First and foremost, I think your wife needs to see someone about this, be evaluated, and treated appropriately. You should also seek counciling together, but I'd make sure this is ok with her personal mental health professional first. She's got something major going on, and she needs to get help with it for both of your sake. If you're tough enough to stick it out and do the hard work, I think the relationship will be stronger than ever, maybe poly could exist in the future. You've gotta find a way to support her through this, even if you guys find you can't be together.
Also bear in mind that if you DO leave her for N at this point, you'll probably have to deal with a shitload of guilt and probably need therapy yourself. So yeah, you're kinda screwed. You're in for some tough times, so I want to wish you good luck. It's not going to be easy, but you've gotta do what you've gotta do. It ain't over till it's over. A bird in the hand is worth two in the bush. Folksy wisdom. Git r done. It's 5 AM, and I'm loopy. My deepest apologies for the previous 5 or 6 sentences.