I think ted27's post is really good.
Though when you say really big, you meant overweight?
If so the only answer is talking about it, getting the child to take autonomy, recognise the difference between hunger and emotional need, understanding the impact on the body of bad foods, and also doing things to improve his fitness. It won't help to label him taking food as "stealing" as ted27 has said.
Talking endlessly about it, really hammering home the medical and physical facts, and getting him to make choices, and making him more aware of how he is feeling and helping him name the feelings, and him being aware that there is a link between feelings and eating, is the only way. Teaching him autonomy and good habits and good thinking rather than making food into something to fight over or hide or be secretive about.
Could you take him running? If you took him jogging twice a week that would start shifting how he feels and how his body feels to him, and is a good first step.
Re how we handle it, we don't hide food or have a snack box which dc can help themselves to, sweet snacks are in one place in the kitchen and the rules are that the dc should ask first and if I say no I give the reason (dinner is in 10 mins), and sometimes I get them to think about it - do they really want it - and tell them it is up to them.
If dc break the rules - and they do, sometimes - they don't lie about it - because there is no need for them too - I tell them off for being disobedient but that is it.
We talk a lot of about sugary foods and the impact on the body and alternatives and reasons why. Over time dc's attitudes have changed as they have grown up. They are more thoughtful and aware of the impact on their body of eating too much poor food when young and they talk about it. Sometimes they still go for the sweet but not at a worrying level.
I am quite assertive about fitness - they love sport and do lessons outside school so there is no worry there but they hate the idea of going for a jog before actually going (as do I) but I force them (and force myself) to go and we all feel better for it afterwards.