OP, I wouldn't start the calorie counting thing for many many reasons. The first being that it doesn't work because a calorie is not a calorie, the second your son is 10, this is madness at any age and at 10? Your son feels different and told you he wants to lose weight and won't take seconds. This is so great, such a responsible behaviour. Praise him and tell him you are going to work and help him. You can empower him at the same time so instead of feeling shit when his friends re stuffing their faces (as boys do) he can feel good. Watch some more movies.
This one has three kids at the center of the story
Another BBC one in Ireland
An american one
and the TED talk from Jamie Oliver
www.ted.com/talks/jamie_oliver?language=en
Watch these with him, and you will understand that keeping giving him a slice of cheese vs a cereal bowl (even all bran) is absolutely the right thing to do . Try stronger cheeses instead a the plain square one. Parmesan, provolone piccante, asiago, old amsterdam , feta, roquefort, these last two in crumble. Make it about flavour
If you have the time, browse your library for Italian cooking books or look online. Skip the pasta and you will find tons of recipes for meat and fish which don't use creams and sauces but use sage or prosciutto. Even in the antipasti /side dishes section, you have nice idea about vegetables prepared with herbs. Such as Cut a zucchini in very thin long slices, sparkle with crystal salt and olive oil and put under the grill . Use spices rosemary, basil fresh, parsley or the ready mixed ones. I use the Aldi mixed herbs a lot. Add rockets to salads, use onions and garlic for the veg. Or even a rocket salad full stop.
About the snacks. Have in the fridge a bowl of cherry tomatoes, boiled green bean, orange slices, lemon slices. Blueberries washed and available. If my kids eat a bowl of blueberries, they don't ask for anything else.
What about teas? I buy herbal teas in bulk from herbs warehouse and my sons like to sip a cup of chamomile or even a fair Darjeeling in the afternoon. You can prepare your own ice tea, with tons of pieces of strawberries, peaches, melon even
frozen berries and some stevia.
I wouldn't force him to do more sports. The diet will make a difference. Having him move more than he is already doing will only make him more famish. What you can do is a big cleanup of your kitchen cupboard. You are doing the whole family including the lean children a favour because it is not about weight but health by removing jars and packets the include sugar.
We don't buy biscuits anymore, but I bake a lot. The difference is when they eat a piece of cake or a crepe, they are satisfied, whereas with cookies, they are engineered so you eat more and more and can hardly stop until the packet is gone.
He is a kid and it is not fun to start a restricted diet, so don't. Just put more colours and flavours and taste on the table. Have him cook with you. Go to the market with you. I don;t know in which country you are but in some countries, the markets are amazing.
I am French, DH is Italian. I have these strong ideas about healthy tasty food, but I guarantee you our house is very popular with both primary and high school kids and whatever I put on the table, they only leave crumbs.