we aren’t meant to be friend of kids but we are there to help guide them to be productive members of society.

so she’s overweight and doesn’t like healthy food, great she can starve to death. Is cps gonna mandatory make you feed junk food? Of course not

yet she uses manipulation to make him believe he doesn't spend enough time with her, 

So sent DH and her off on a daddy/daughter camping trip! In fact, send them off on some great adventure all by themselves EOW.  Don't be a cool friend to her, have her get her own friends and go do things. You should have friends too and take off to spend time with them when she's there.  I'd be completely hands off about her diet, that is totally daddy's domain.  

I used to have people do the "just be their friend" thing in the beginning.  It came from everyone from total strangers to the multiple counselors to whose offices I got dragged to hear about what a terrible person I was for daring to exist and how I needed to "put the members of the first family first."  (Gee, wonder why I have such contempt at this point for "family and marriage counseling?")  I was quite clear that as a grown woman I do not have children for friends and the people who do are creepy as hell.  Let's just say that I did not make points with that attitude.  People would just sputter and say "well, I don't mean friends....I mean...well....uhm..." but they could never actually define what they wanted me to be.  Or do.  Or say.  Just not what I was being, or doing, or saying.  So in other words, just go away and magically music will swell, birds will sing, and the parents of these children will fall back into each other's arms for all eternity.  (Or the kid's wish could come true and I could get hit by a semi-truck.  LOL)

You are doing nothing wrong.  You can't be friends with a 15 year old girl.  I would be willing to bet that even her own friends really aren't friends.  Teen girls are horrible to each other!  Just get through this as best you can and give her as much alone time with her father as her heart desires.  Make your own plans and let him deal with her all by himself.

I’d skip out on the next camping trip.  Camping or just going on any vacation with DH and SD without my bios would be my worst nightmare.  My SD is obese as well, I gave up caring about what she eats or doesn’t eat a long time ago.  That’s completely her dad’s problem.  

Then your DH takes over as friend. Why do ypu bare what she eats.  I would just make what I normally make, 

Unless SD has health issues contributing to her weight, that obesity is a manifestation of their family dysfunction, specifically codependence, as in keeping a family secret (the kid's obese!) that is not a secret at all.

I mean, when you see an overweight dog, you don't say the dog should choose to eat smaller portions, right? You don't blame the dog for not spending enough time at the gym? No, you look at the dog owner and wonder why they'd indulge a pet they claim to love to the point of shortening its life.

And that, MsNiceGuy, is why you are off the hook. They were all a mess before you got there.

Mom & dad are probably convinced the kid's weight is a direct result of their failed relationship. So instead of screwing up once by splitting up, they screw up twice by splitting and then letting their kid's obvious health crisis slip through the cracks because no one wants to talk about the elephant in the room if it means they might hear they're to blame. And if no one will talk about the elephant, the elephant will never lose weight. That's the family secret that isn't secret right there. Creepy...

Their daughter's weight is an OBVIOUS SIGN OF THEIR FAILURE as parents, so you deserve no blame for the kid's sour attitude. How would you feel being fat like that and even your own parents don't have the balls to help you figure out how to fit in better, feel better, look better and have a better future life??? They are all really, really dysfunctional and that's how you have to start seeing them if you want to sort through your role in this. 

I also tried to play it hands off with SD and when she still hated me no matter what, I wondered if I was cold or too distant, neither of which I am under other circumstances, so why even ask myself that? Stepmothers just can't win.

And that's what I'm saying... Look at the obvious signs of serious codependence among this BM, BD and SD that's manifested in SD's weight...that no one is talking about... why would you ever ask what you did wrong to make SD dislike you when there's already so many damaged players in the mix?

First off, I would not go camping with a skid that hated me. DH can take her by himself.

Second, let her eat herself to death, it's not your problem, whatsoever.  Let DH deal with it. 

Third, trying to control food choices and portions with overweight kids just makes them sneak food.  That doesn't mean you have to let them eat endless junk food, but nor do you have to ban junk food entirely. 

Is normal custody Every Other Week (EOW) or is it Every Other Weekend (EOWE)?  If it's the former then she should not be so starved for dad's time.. he should be able to give her plenty of attention on the weeks he has her.  If it's EOWE?... she does have a point that she doesn't get much of his time and he should be spending MORE time with her on those couple of days a month than he might spend with others and doing other things.  Does he keep in contact with her much while she is at her mom's?  My DH used to text and talk with his DD's when they were with mom.. just to be involved and present in their lives.. even if he couldn't be there physically.

Unfortunately, he can't pay his way out of the fact that he can't be with her more.  He needs to accept that and not parent from a place of guilt.

I think when people say that you should be her "friend".. they mean a bit more in the realm of you shouldn't try to be her mother/parent.  Leave discispline etc.. to your husband.  Maybe the "friendly Aunt" level of relationship.  Not super close.. but able to do the occasional fun thing together.. and be in each other's company.

Her weight and health are unfortunate (as are mine.. though my DR tells me I'm a very healthy overweight person.. no pre diabetes.. no blood pressure or cholesterol issues etc).  But, if she is only in your home for a couple days at a time normally (I am assuming you meant every other weekend since the weeklong camping was an exception).. I would actually not get overly involved in trying to make her eat right.  I mean, I might make sure that there are healthy options available, but I would probably still have things I knew she could/would eat there too.. maybe not the worst junk food offenders.. but mac n cheese?  I'm not dying on that hill. 

Being SD's friend is what got her in this mess to begin with. Both her parents chose to be her friends and now she is an overweight co-dependant child who believes it's every adults job to entertain her and keep her happy.
Cooking healthy meals is a nice idea, but the kid is only going to lose when and if she finally wants too.