Some girls and guys are certainly worth the effort, once you get to know them....but of course, if you haven't even seen them yet, then this much anxiety over someone who doesn't want to show you their picture at the least, is a bit ridiculous.
I'm beginning to suspect that the OP may be the one with self-esteem issues or at the very least also have some assertiveness issues. After all, any one who gets to know someone over a 2 week period and is denied either the ability to meet up with someone before investing more time, or being able to put a face to the person they're speaking to intimately, doesn't perhaps either have enough confidence in that they can do better, or is a bit of a 'doormat' themselves, or doesn't have enough self-esteem to feel they deserve to put a face to whom they are speaking with and to assertively, but politely ask that though they understand the other person's explanation and concern about not wanting to give their picture, they aren't comfortable with pursuing a relationship with someone who isn't able to be upfront with them about who and what they are currently.
This is a childish and immature game being played by this girl. If she really respected the OP she could simply and easily tell him that she doesn't look her best at the moment but that she's currently taking the steps necessary to become healthier and that she feels that withing a month, or whatever projected time-frame she thinks is doable, she should starting looking and feeling better about herself, and hopefully more attractive to the OP. That's what a normal person would do. That's how some girls over the years have discussed their feelings towards themselves with me. It's not that they weren't good-looking but that they didn't feel 'good' or confident about their appearance and they were upfront and honest about it...and I gotta tell you, and everyone else, since i'm using your post to not only reply to you and the OP, but also address the readers at large; that I appreciated how they felt about themselves(we all have something physically that we don't feel terribly attractive about) and the steps they took to feel better and more confident. It showed me many things about them....the least not being self-confidence in identifying and understanding that physical attraction is healthy in a relationship and being honest about themselves and having the character and discipline to go out and affect some change in their lives. I always appreciated that about some of them, as I know they appreciated that I took care of myself as well.
This whole nonsense about needing time before showing a picture or meeting up is just that....nonsense. It shows immaturity and a level of distrust of her for the OP.....and no healthy relationship can be built on distrust. This girl is immature and has more issues than the OP should care to deal with.
I recommend once again, that he assertively but politely make it known that he'd like a picture, with the understanding and tact that lets her know that he understand where she's coming from, and that he's not that shallow to stop speaking to her as she undergoes whatever fitness or beauty regiment she feels in necessary for her own self-confidence. If she doesn't trust him enough to meet or send a pic, then once again the only recommendation I have is "run".