Kids don't get enough to eat at school. They get all of 10-15 minutes to get in line, select their food, find a seat that's with their friends, get their food all arranged (like buttering the bread and stuff for adults), actually sit and bite, chew, and swallow, their food. If you could hide and watch the lunch room at a busy elementary school you would see. Then they go play , go to class, have recess, get out and come home with having had little food since breakfast, and did they even get to eat a filling breakfast?
Kids need more calories than adults and adult mealtimes don't work for kids either. If you eat between 5 and 6 pm then he needs a heavier protein snack with whole grains. Then he is also going to need a snack around 8-8:30pm. If you eat later, say 7-8 pm then you need to fix him a meal for after school snack. He is starving when he comes home and you're only giving him a couple of peices of fruit. Which is used up nearly immed.
If you feel you have very valid cause for concern then please talk to your pediatrician. Tell him your child has unquenchable hunger and have him tested.
I, too, have food put back for certain meals and get upset when someone gets into it. We live on SSI and make too much money (they classify it as unearned income) for food stamps, if it was earned income we could get hundreds of dollars a month in assistance. So my food budget is tight. You need to put that food up or go by it every other day or so. He needs a place he can have snacks that are approved by you where he can go get something to eat. It will take some time to teach him how much he can eat and that it has to last until you go to the store again.
My friend has a pull out cutting board in her kitchen. On the counter beside it she keeps whole wheat tortillas, peanut butter, rice cakes, oatmeal bars, etc...and in the fridge she has yogurt with fruit, shredded cheese, grapes, strawberries, etc...she has taught the kids to make cheese casadia's by putting the shredded cheese on the tortillas and heating it for 23 seconds in the microwave, they also have individual serving size microwave popcorn the can cook. They put it in and select the little picture of popcorn and it auto cooks.
BTW, her kids are 6 and 8. They have been fixing their own snacks and lunches for a couple of years. I don't let mine do as much as she does but it works for her.