My wife is a clinical nutritionist and a psychotherapist. She has told me, "there is a lot of psychology in nutrition, and a lot of nutrition in psychology".
More specifically, it takes a healthy emotional state to direct oneself and respect boundaries. ( Personal and those of others. So many folks try to undermine the healthy eating of others, this is a challenge to people who vary from the system that formerly supported their unhealthy eating, drinking, substance abuse, etc.)
At the same time, emotional/psychological health is dependent upon sound physiology, ie; brain chemistry, hormone levels, etc.
If one is seeking ONLY information, then the obese nutritionist is like a book. If any level of support is involved, personally, it would be too much of an obstacle, just wondering about this question. I'd rather avoid the issue and just find someone who "walks the talk". Yes, in some fields great coaches are not great performers. I don't think that applies to a lifestyle matter.
My wife looks great and on top of her multiple degrees, it reinforces a patient's belief that she lives what she teaches, and of what is possible.
( "Metaphysically", an obese nutritionist, IMHO, is sending a message of failure.)
All the best,