Op, it sounds like this young woman is not happy or very comfortable in your household and company. Turning down family sit down meals (although late) and movie nights, are contrary to the au pair experience. She sounds to be alienating herself. This is more worrying than the food part, which may be comfort related. Two chocolate bars is one evening is not just greedy and unhealthy, but surely not normal behaviour. She is not attempting and accepting your offers for her to be part of the family, but being very free with the communal food and snacks. Her actions are a bit at odds, as surely you would establish yourself so you can do things an established member of the family does, like being liberal with food. Is she leaving any snacks for anyone else, seeing as you say she takes more to her room?
Boundaries are needed here, but above all you certainly need to sit her down and ask her how she is feeling being in the setting she is in as this may not be about food.
Are you in an urban, suburban, or rural area?How big is your home?! Does she have a clear space for herself where she can make noise and not be heard, and bring friends to socialise?! Or is it just a room in your home where she uses the same entrance as you and all goings-on can be heard?! Does she have any friends?!
She may very well be unhappy and homesick, or lonely. Or a mixture of those. How long has she been with you OP? Does she attend English language classes?!
I was an au pair in Switzerland 8 years ago and lived with the family, so I know how it feels to be in this scenario. Luckily for me I was in a city with lots of other au pairs I met a few times a week, I had friends and things to do outside my shifts, and I always accepted offers of activity with the family which made all of us comfortable with one another and made it easy for me to call their home my home. I ate what they ate together with them, which was lucky for me as I was not the best cook, and they ate very healthy. I.e. Steaks and salads, roasted chicken and vegetables. There was lots of fruits and no 'snacks' in the house except an occasional pack of fresh macarons which the mum thought was a once a week sweet treat for the family and myself (I felt grateful, as to me they were posh and expensive and I could never afford to purchase them myself on the au pair allowance). Perhaps my open easygoing personality played a part in creating this home away from home feeling I managed to experience. Who knows?! Nevertheless, I rarely felt low and a need to retreat to my room, which was private in the loft with my own shower, and great soundproofing, which meant I felt when I needed my space I could easily have it without worrying about being in the family's way, but never felt like I needed to exclude myself from them. I was very lucky.
Please have a heart to heart just to see if the over eating, as you say she also eats with the kids, and has extra snacks, is perhaps a sign of unhappiness and homesickness. If so, discuss together what can be done to better the situation for all involved. Even if only sending her home for a short weekend if you can afford it, or buying her a gift to show your extra gratitude if you don't already do this. The little things can make a world of difference in these kinds of situations, and may lift her spirits.
If this proves to not be the issue, I agree with others that a weekly meal plan drawn up together, could really change things for the better, without ever bringing up your concerns over the food. I am not sure about the snacking. You may have to approach this one with a bit of tact.
Keep in mind that au pairing is meant to be a cultural experience where you are an actual part of the family and do things with the family. Whilst she shouldn't be forced into activities, she should still be part of them, and turning you down is contrary to the purpose of coming into your home to be an au pair. Wish I could be of more help. Good luck.