First and foremost: do not make a big deal out of this until you know what's going on. You wouldn't want to put bad body image on her, or lay the groundwork for an eating disorder later on. As one mom mentioned, later on so many girls WON'T eat because they're scared of either getting fat or looking like a pig for eating in front of friends. Ridiculous! Don't be a part (even inadvertnently) on that developing.
I suggest talking to the teacher and asking her to tell you what she buys and if she eats it when you see her later that day. If not, go to the school and make it a casual thing where you just go and eat breakfast with her there. See what the breakfast menu is and what her natural choices are (just observe, so you know what she's doing when you're not there), and see if she eats most of it. I HATE eating breakfast early in the morning, so I have a piece of fruit and that's it. I simply won't finish a larger breakfast. A banana obviously isn't going to hold me over all morning, so I eat again a little later. That's how some people's bodies work.
If it's "junk" or "fun" food, I'd allow it maybe once a week, on a Friday as a reward if she was good all week or something. If it's normal food, then by all means don't argue with it. You can adjust your budget and menu as needed. Instead of cheesesticks, you can buy block cheese when it's on sale and slice it. One slice, then cut in half, is 2 sticks! Instead of buying single yogurts, pick a flavor for the week and buy the larger container of it. That way you can serve a couple scoops that she'll actually eat instead of wasting a container she won't eat all of. Things like that help, and I'm sure you can make up $5/week and still allow your daughter a little social time and the healthy habit of eating 5-6 small portions a day instead of 3 large portions. And if she IS severely overweight (NOT talking "baby fat") then consult a doctor to make sure you get a plan for HER NEEDS not yours (children have different dietary needs and shouldn't just be stuck on a diet), and do things together that are more active then tv and video games. Make it a family change, not something put on her. If she's healthy though, I'd be perfectly fine with this.