I once knew a family who tried to eat mostly vegan meals. Their oldest daughter was quite heavy, from well before their decision to remove (most) animal products from their diet. The mom believed their veganism was really healthful, because in her words, "can you imagine how <daughter> would look if we DIDN'T eat this way?!" I kinda imagined the girl would look about the same no matter what, but the mom figured the girl would be twice as big without the vegan diet.
A vegan diet isn't necessarily low-calorie, low-fat, or even nutritious. Like anyone else, vegans can choose to eat a healthy variety of fresh whole foods, or a diet of junky fatty sugary processed foods, or any combination of those things.
Btw, I'm vegan and average size. I've never been thin in my whole life, and I didn't lose or gain any weight when I went vegan.