She ended up losing about 10 pounds of fat, and looks AMAZING.
There was just one thing holding us back from a relationship, her ex. She is still attached (she claims its love, but she is just attached/lust) to a guy she dated about a year ago. I've asked her, and she said they don't have a sexual relationship anymore, and are just friends, but she still "loves" him.
Dude, these are the 2 things in your original post that raise the most red flags for me. Please keep in mind that I'm among the older people writing in this forum. That should raise a couple of issues, like: people have changed in the years since I've been on the dating market, or, I've never met this particular girl so how can I make judgements about her.
There may be others and they probably all are true so be prepared to disregard what I say as total bs. But I am relating the reality of what I have seen and experienced while "in the market".
Item #1: The fat issue. I would have to wonder if she got dumped by the ex because he lived his romantic life by the "no fat chicks" rule. This may be important. If he dumped her she clearly has unfinished business with him and it could run from "I'll get back in shape and show that a$$hole what he got rid of" to "oh God, I am so miserable without him, I'll do whatever he wants just so I can be Mrs. so and so and have all his babies....." This issue with the body fat could have happened before and she is living he vengeful life, taking it out on every guy she can. I kinda doubt this one but I've seen it before and it's toxic. Don't get any on ya!
Item #2: "She still loves him." She said it, not me. Clearly this is a DANGER sign in big red letters. Don't ignore this. It will undoubtedly be the undoing of any relationship that gets forced with this girl. Even if you pursue from a distance or play coy and stand back and wait for her to see what a good guy you really are are you really ready to spend your time at the office wondering why she's not answering her cell phone? And she has given you more than ample warning that she will be thinking about the ex whenever she has a little down time.
Based on my own experience both in the dating world and in police work I would say that the best thing to do as far as this girl is concerned is to put down your expectations of ever having a happy life with this one and back away from them. I say this for two reasons. Based on what I've seen and experienced any relationship that any guy but her ex has with her stands a high probability of a rapid crash and burn scenario at the end of it. (Picture yourself in the green room at the Jerry Springer show). And because you are going into law enforcement, dude, you need to have your wits about you at all times on the job. You cannot afford to be wondering if she's being faithful to you while you are on the midnight shift too far from home to do a drive-by to see who's car is sitting in your garage. (I put it that way to be a gentleman). I would do some major distance from this chick and when I see her number on my caller id I would hide in my closet.
Remember the old adage about the guy who found the frozen rattlesnake, took it home, nursed it back to health, only to have it bite him. When he asked the snake how he could do such a thing the snake replied "I'm a snake, that's what I do". You can't change anybody, that's a job for the shrinks. Take care of yourself first and foremost. Find a woman that you can be HAPPY with, not one that you know is gonna stress you out every chance she gets.
But I'm a crusty old fart and I may be wrong. Keep us posted.