You might want to suggest she tries reading about it to learn more. Or suggest that you do it for a few weeks and she can see you're not eating unhealthily and can witness your happiness increase as you lose weight (if it does). Would she really be happier if you were doing one of those stupid diets like only eating grapefruits or something? Reassure her there is nothing wrong about eating whole foods, cutting out sugar and processed crap and you still can eat vegetables.

That said, the incentive to lose weight should NEVER be about your friends being skinnier than you - we are all made differently and its not a contest. Make sure you're doing this for the right reasons.

At the end of the day, you are an adult and you choose what you put into your body and what you choose not to. Good luck!