I came across this concept when I was reading various web sites, working on getting motivated to start making healthier choices with food.
Basically, it's all about being compassionate and loving with yourself. You write a thank-you letter for all that your fat has done for you and that, while you love and appreciate it for doing its job, you don't need it anymore. It's a really powerful exercise.

I'll get the ball rolling. Hopefully, others will want to share their letters and we can get a really interesting discussion going.

Dear Fat,

Thank you for shielding me and offering me protection from the world. You have been there for me as a comfort when I was afraid to be thin and suffer the implications of what being thin meant. You shielded me from unwanted attentions from lascivious men, and you were my comfort after I escaped from a terrible relationship with a controlling boyfriend.
I know that you are just doing your job. I appreciate that you have been here for me all these years.
But, I don't need you anymore. It's nothing against you. I just choose to respond to stress and the pressures of the outside world using my brain and not my body. I have found new ways to cope with feeling vulnerable, and I thank you for being there for me before I learned these new ways to cope.

Love,
Me