1/ You can get fat first and become vegetarian after
2/ A vegetarian diet isn't that restrictive. Cheese, eggs, olives, nuts, vegetable oils in general, sugar, processed cereals, processed bread, candies, sodas, vine, beer are all vegetarian options and if you eat too much of it and don't work it off ...
The vegetarian lifestyle isn't more unnatural than the average american diet. The average veggies in the US isn't swapping good quality animal products for over processed fake meat, it's swapping overprocessed meat mixed with additives, soy, corn, canola oil and wheat for something pretty similar with just the small percentage of meat removed.
We can get a lot of great nutrients from meat and fish, but we certainly not evolved to eat it everyday like we do on average. It does clog our arteries to eat as much animal products as we are currently doing, not to mention the problems with overfishing and lifestock burping so much it's ruining the atmosphere.
Your fat vegetarians probably have an issue with portion control.