I have a tall, heavy four year old DD. However, she is not overweight, (I think 80 percentile) just a large child. Her dad is 6ft2 and stocky, and I am 5ft 8 and size 12 so she was never going to be little. You can tell that she is healthy, just solid, not an inch on fat on her to pinch. Clothes size 6.
What stands out from your posts and responses are: if he wants things like ice cream, why do you have them in the house? Same for biscuits, crisps, sugared cereal and all other rubbishy food. I don't buy it in our weekly shop, as its not something that I want us to be eating. Once a week DD goes to her grandma's for tea and eats the lot! Chocolate sandwich, ice cream after tea, but she knows that's not how we eat at home.
He definitely doesn't need a sandwich before bed! At 4 that's like a whole extra meal. There's nothing wrong with him snacking on healthy foods, and eating his tea a bit later so that he can last til bedtime.
As parents we associated food and feeding our children with care and love, and being attentive to their needs. However, food is sustenance. Food is for energy. Not comfort, not rewards, not incentives, not bribes. If you offer him a healthy food and he says "no I want X treat" then he is not hungry. Unless its something he really doesn't like (but you say he likes fruit and veg) then if he's hungry he will accept what you are offering. You are the "keeper of the food" and its not up for barter or discussion what he can have. It's nice to give some leeway of course, on Wednesdays our DD gets to choose what the whole family eat.
How is your own eating? Do you eat with him, sat at the table etc? Does he see your food portions, see you enjoying fruit, drinking plenty of water etc? They take more cues from us than we realise. A case of practice what you preach! And make eating a positive moment for talking about your days, learning about the food on our plates. DD loves knowing what her food types do for her body.
For perspective, DD who eats like a horse and would eat all day long before we made the types of changes I'm talking about now has an average day something like this:
7am Weetabix with almond milk and banana
Glass of water
10am (at school) piece of fruit and palm sized turkey ham sandwich
12pm (at school, not in UK) 3 course, portion appropriate lunch. Here the menus are designed by a nutritionist, who signs them off monthly and they are emailed to parents with a break down of the protein etc and a suggestion for tea to make a balanced days food. An average lunch might be something like fish soup, followed by french omelette and salad, and fruit for dessert.
4.30pm coming out of school snack. Piece of fruit (first) and then a treat, either a few biscuits, croissant, homemade flapjack etc.
6pm tea, something simple as her main meal is at lunch, on the weekends we do the same. Pasta carbonara, Chicken burger meat and veg, Small baked potato with cheese and beans, Sausage casserole, rice with a tomato and a friend egg. Then fruit, a soy yogurt, and that's it until bedtime at 8pm.
In between times, fruit is unlimited. Sometimes if I can tell she is actually peckish rather than bored or attention seeking, we could make fruit smoothie, or a fruit platter for sharing etc.
Physical activity: judo for an hour on Tuesdays and again on Thursdays, in school lunch break. Same for gymnastics on a Friday. Walking to school and back 3 times a week (15 mins walk), plus park/beach walk / football in the garden etc as and when.
Please don't think this is a huge sanctimonious post, its just an example of another big eater four year old without them being overweight. She still eats double what some of her classmates do, but its healthy, in line with her constitution, and most importantly, keeping a positive relationship with food. Please feel free to private message me if you want to chat more