I wrote quite a bit on this but accidently hit escape and lost it all.
I was in the same situation as you were. I was with one of my ex's for almost 4.5 years. She was much like your SO and would get down on her self for her weight and appearance. No matter how much I would compliment her about her and her body (including the specific things I liked about her) it didn't seem to help.
I encouraged her to seek help or at least be proactive about it. I would excercise or eat mor healthy my self as an example. I woudl tell her daily how beautiful I thought she was (is) and tried anything else I could think of.
It seemed to me that no matter what I said it had no affect on her. When I would tell her this "my words and feelings don't mean anyting to you" she would say two things "you have to say those things, your my boyfriend" and "yes they do, I would be much worse off if you didn't." Despite this encouragement I saw no improvment thus telling me that I didn't have any affect.
Well we broke up about a year ago. Since then we have figured out something important. During our relationship I acted like a crutch for her in this area. Once we broke up she took stock in her life and realized that something had to change. She has since taken a very proactive stance on this and has started to lose some of the weight that she felt she needed to. She is happier with who she is and has more confidence.
What it came down to is that your self esteem is something that you have to work on, and when you have a SO who will tell you what you want to hear (even if its absolutely true) it is hard to really get motivated to change what you don't like. When we broke up we realized that we only had ourselves to rely on at that point.
This made us both make some important changes
This is just one man's experience and please feel free to PM me if you want to talk further on this with me.
Good luck, I know how hard it is.
O, and look into a different counserlor. They are pretty hit or miss from my personal experience.