Adopted children and food obsession?

I have 3 wonderful children. Two are from china. One was adopted at 11 months of age and had a VERY hard transition. One was brought home at 2.9 yrs of age and had an easier transition. BOTH seem to be food obsessed. My daughter who was adopted at 11 months did hoard food. It was typically food she wasn't allowed to have often like candy. I would find the wrappers. Then chips, etc. That behaviour has subsided somewhat but she and my other adopted son are OBSESSED with food. I mean, she could be eating a meal and then ask when her next one would be. He hovers around food constantly. She has a cholesterol problem, so we need to watch what she eats a bit, and he is getting to be quite portly. He will ask for 2nds and 3rds on meals. I'm not sure WHAT I should be doing. I started a "snack" draw filled with healthy foods in the bottom of the fridge. Apples, nuts, yogurt, cheese, etc. Now the snack draw is an obsession. They could go in and grab something and then ask for another snack immediately after and keep going. My biological son doesn't seem to exibit any of this behavior. He eats his meals and typically doesn't even think about any more food unless he really is hungry. He doesn't ask when his next meal is when he is eating. So, how do I handle this? There isn't a lot of information on the internet. Her cholesterol (she is 5 yrs) and his chunkyness (he is 4) is a bit of a concern in how to handle, yet not have the focus always be on food. Any suggestions? The snack draw backfired immensely. Now what?