I agree with everyone else. Don't date her under the condition she work out more. BUT I think you should start even slower than asking her to the gym. Start with telling her you were thinking about how she wanted to change her lifestyle (not specifically the weight thing) and say that you were thinking you can help each other out. You can help motivate. Her if she wants it, and think of something she can help you with (not just physically but there has to be something she's better at that you can open up and be vulnerable to her to). Weight is a big issue for any girl, add in the fact she most likely has a crush on you and this is a recipe for disaster, especially if you start suggesting she lose weight in order to be with you.
Maybe start slow, seeing what she wants to change and what she wants help with. She's tried and can't stick with it... That means she isn't ready. When you are ready, you just do it. She may not be ready for a drastic change, but she might be willing to go for walks/jogs after work, take a healthy eating class. This has to be on her terms because otherwise she will feel judged. I'm sure she already does if she's comparing herself to your other girlfriends. Girls are their own worst critics, so if a guy she likes tells her she is too fat to date you are absolutely going to lose the friendship you have. Even if you stay friends, it will never be the same. Until now, you have not expressed any interest and suddenly a guy she considering friend and potentially likes is telling her she's too fat? That's kinda devestating. Seriously, start slow. She'll never get over it if you don't.