It is not possible to motivate another person to do something. You can't make an addict stop using, you can't make a smoker quit, you can't make a person take medicine or get therapy if they need it, and you can't make someone exercise and eat better.
If her attitude and appearance are a turn off all you can do is get out. Even if you love her. She might wake up and decide to change her life. All you're looking at is the shape of things to come if you stay with her anyway. She's aware of her shape, she knows how to exercise, she's not blind or ignorant, she's unhappy with some aspect of her life and it's coloring everything in her life. Lack of exercise isn't the disease, it's a symptom.
I kind of disagree, and agree. You cant help someone unless they are willing to help themselves. BUT! You can motivate and push to an extent, I actually just posted something Very similar to your situation minus the complaining and such. She does bitch about it sometimes and I respectfully reply with "Then do something about it" and thats it. Leading by example works too only if your not in the best shape either. Its going to be kind of difficult for you to lead since your already a trainer, so its nothing new for her in that aspect.
Ultimately if you love the girl then dont give up. Shell come around, maybe there is something else thats bothering her and she just needs a moment if clarity (sorry I know thats kind of an addict statement) but maybe its true. Love her, make sure she knows your behind her and willing to help out when shes ready. Thats it, the ball is in her court.
Then again, if your not THAT into her then go now and don't waste either one of your guys time. (i know this is the women's portion of the forum I just had to comment cause its all to familiar and thought maybe this might help) good luck and I really hope it all works out : )