The Background
I have grown up in a very athletic household. Every season, a different sport. On vacation, our family would constantly be biking around, swimming at the beach, skiing in the winter, hiking in the spring and fall.
Growing up, I resented this, but today I am incredibly grateful for the passion for sports, athletics, and outdoors that my mother and father instilled in me. Growing up, I was a bit chubby, but now I have found sports that I love, that fit my lifestyle, that allow me to be in good health and great athletic condition. I am happier, healthier, more confident, and more comfortable in my own skin.
My father is an incredibly blunt and forceful type A personality. A leader at work and at home, he expects obedience in all facets of life. He has an idea of how every person around him could change to suit his liking. He is a loving, caring, and good man at heart, but with a very "my way or the highway" philosophy. I again used to clash with this during high school, but have since come around to many of his points of view, acknowledging that he is right in many cases, despite his harsh and tactless delivery. Living and interacting with him, I have been forced to learn how to work and communicate around problems I cannot face head on, around people I cannot change.
The Problem
My sister is much more like my father. She is strong willed, hard working, intelligent, and motivated. She has always clashed with my father due to their unwillingness to compromise and make peace. She has a good job, a good boyfriend (my father would disagree of course), a good degree, and is happier than ever. However, she has always been a big, much like I was growing up. After high school, she stopped participating in high intensity athletics, and has gained some weight. Out of our family, she is the only one who is not in good shape, the only one who does not participate in high intensity athletics 4+ times a week.
She is obviously uncomfortable with this, and tries hard to be healthy (to limited effect). Every time my sister comes home for holidays, there is conflict on this front. My father will bluntly and honestly tell her that she could lose some weight, that it is unhealthy, etc. This leads to big fights, where my sister will yell about how dare he bring it up, how hard she tries, etc, and my mother will come in to protect her kid.
My father blames my mother for being an enabler, and it hurts their relationship. It obviously hurts the relationship between my father and sister, who otherwise have been getting along much better since she moved out. It hurts my relationship with my father, as this behavior is unacceptable and uncivil.
I do not want to tell my sister what to do. I do not want to tell her how to live her life. I do want to resolve this conflict that is damaging my family
The Solution
By (the absolutely crazy) American standards, my sister would not be considered particularly fat. However, I am sure she wants to lose weight and be healthier. She has stated to me personally, and to my family at large, that that is a goal of hers. My father wants this, I want this, it would be a good thing. However, I believe this conflict makes it less likely that my sister will be able to make this transition.
I cannot change what my father will do, what he will say, how he will act. It is not feasible, and I do not wish to attempt to due to the conflict it will cause. I don't really know how to move forward. I am worried that any attempt to reach out to my sister on the subject will immediately be interpreted as an action of my father (and she would be right, he has often asked me to take his side) and rejected.
Is there a solution to this problem? I have thought about talking about my own experience, changing my diet, my portion sizes, and finding athletics that I enjoy, but I don't know if it will work.
The easiest solution is for my sister to cut contact with my father. It is what I had planned to do when I was in the same situation. Is there a solution that will not damage our family (however deserving this damage is)?
I'd also like to say that I have been largely silent on the issue, not attacking my sister as is implied in several answers. I would like to intervene, but I do not know how.
Edit: If there is anything I can do to improve this question, please let me know. Please do not downvote without giving me the opportunity to improve my question.