Perhaps the child is "overweight" because she's on medication - had you considered that, @Geraniumgal ? Maybe her mother is "morbidly obese" because she's on steroids...?
Honestly, and I say this kindly, you know jack-shit about this family and their life together. For all you know, the child was grabbing the biscuits and cake because she doesn't get them at home, and therefore, no; she wouldn't have wanted the sandwiches and carrot sticks. My stick-thin daughter used to do this at that age, at birthday parties... but because she was slim, no one ever commented on her behaviour, other than to wish me well with the inevitable sugar crash! At home, though, her diet was meat and veggies, few snacks, lots of fruit, and water instead of juice or pop. My choices as a parent went out of the window at children's birthday parties, though... as I'm sure every parent who doesn't hover round the rampaging hordes trying to give them complexes about never eating things like cake and biscuits (or, you know, disordered eating...)n will testify to!
(What child in their right mind does want fucking carrot sticks at a birthday party, for fuck's sake?!)
Just the other day, I had the mother of one of my 18 year old son's friends take me aside and tell me that my son is anorexic - when... dear gods above, no. He eats for England and then some... he just happens to have had a lot of upwards, rather than outwards, growth-spurts. But they made this assumption because... they only ever see him wearing baggy hoodies!!! Fair enough, she was concerned - but she's also one of the "unkind mothers" who clique together at the school gates, who thrives on creating drama. If I'd been in a less-kind mood, myself, when she told me this... I could have told her a few home-truths about her own son and his behaviour (steroid and cocaine abuse, not to mention that he beat up another boy very badly a few weeks ago, and regularly fucks around on his long-term girlfriend) but not my circus, not my monkeys. I strive not to lower myself to that same level.
In short? You worry about your kid and your weight. Keep your beak out of other people's business unless you have categoric proof that there is genuine, actual abuse going on,