She is unhappy. Nobody triples in size and overeats and abuses their body because they are happy and balanced.
She will know that she's gained weight and chances are she realises you're avoiding sex. She might be avoiding it too out of self consciousness.
You really can't broach the subject of the weight without being hurtful or patronising. She knows. All that will do is make her even unhappier and prompt her to continue overeating and not taking care of herself or her body.
What you can do is broach the subject of her unhappiness, what is making her unhappy, and what you can do to support her in that. That's the real problem. The weight is the symptom, not the cause, though it'll have the effect of tying her into a vicious circle, since being overweight will make her unhappy too.
If she mentions herself, unprompted, that she's unhappy about her weight, that's when you can start to show your support for healthy eating and exercising too. Don't expect her to change her lifestyle without changing yours too. You'll need to be with her in cooking healthy meals, finding alternatives to snacking, exercising together (if she likes that - personally I like to exercise alone but many people benefit from company and support, especially if they're new to it). Be prepared to make changes with her.
Good luck.