I have two gannets. At your DD's age, my two would begrudge every mouthful I had if they'd finished theirs. Apparently it was the same when my DB and I were small, so my DM would always add more to my DF's plate for us to legitimately scavenge from, after we'd had our own (we thought it tasted better from his plate)
My DD can still pack away an enormous quantity of food, but because she does a lot of exercise / she walks to and from school / extra curricular activities etc, she does not have any excess flesh and is muscular.
My DS has just turned 3, he regularly helps himself from the cupboards, fridge and the fruit bowls and drags a stool to reach. Most of the food items are healthy, he also walks for up to 1.5 hours a day, so I think he burns most of the calories off. At your DD's age, my DS couldn't be trusted near the cat's food either 
Ensure your DD has a decent breakfast: porridge, toast and fruit. Lunch can be eggs or soup, plenty of bread or a sandwich, yoghurt or more fruit. Dinner can be pasta, rice, cous cous etc with plenty of meat / vegetables, grated cheese and rice pudding or fruit. I don't offer the other items unless the main meal has been finished or a good attempt made on it either.
If you are offering apples, celery batons, carrot sticks, rice cakes and bread sticks etc in between meals, this should reduce some of the cravings for sweet stuff, cake or crisps.
If she is getting plenty of whole grains, protein and fruit she should feel fuller for longer. Try not to give too much fruit juice or refined carbohydrates such as biscuits as they give a sugar high and will make her hungry quicker. I'm sure you are doing all of this anyway. 
We always have breakfast and dinner together at the dining table, eating together is important for us. Their manners are terrible though and I can't get them to use cutlery properly yet
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I agree, It is perfectly normal to eat chocolate etc when DC are in bed / not in the same room etc.
Good luck and don't worry too much. Once your DD can go for walks with you for longer periods of time, any excess will come straight off and you will be able to distinguish appetite more clearly.