This is tricky, it sounds like her comments could be caused by any number of things.
1) She is trying to be empathetic and helpful, but it is not coming across that way.
2) She might really be that down on herself, even if you don't see why. Remember that just about everyone has body concerns, even if they don't seem to you to need to be concerned.
3) She could be deliberately trying to undermine you.
I'm sure there are other options and many in between these three, but it's hard to tell based on your post what her motivations may be. I know I would get upset with someone who said we were the "two fat girls" as girlpiggy described, even if the intention was to create a stronger bond. I think that's what it comes down to...how you are feeling about her comments. I think the next time she makes some comment like that, take a deep breath and tell her how it makes you feel. It's not really your place to get upset with her when she eats cookies, but you can tell her how you feel when she tries to guilt you into eating one too. Maybe try to be a positive influence on her?
"You know how hard it is for me to stay on a diet, and that my diet plans can get completely derailed if I have even one cookie. I always feel so guilty if I eat a cookie anyway, that it's best to just not eat one. But if you don't feel guilty then feel free to eat the cookies, you can enjoy them even if I don't eat any." Or something like that. Have something ready to say when it comes up again. Eventually she might get the message.
Maybe propose a little friendly weight loss competition...Biggest Loser Style? One would have to buy the other lunch after a month, whoever has lost the largest percentage of weight? This would cause you to both focus on weight loss plans.
Finally, if you feel she is purposefully trying to undermine your weight loss attempts or put you down, that is not something you need in your life. If that's the case, I'd dump her.