Struggling with being the Mommy today

I have an over eater in my house. Addley would eat all the time if I let him. He drinks alot, he eats alot, he plays alot. We have never been overly concerned with his eating before. Recently though I have begun to worry about him. Paul is a big guy. We have no doubt that Addley is going to be a big guy as well. I'm just trying to walk the line between him being an OK big kid and staying away from truly unhealthy. The problem that we run into is that Addley is quite literally a closet eater. He will sneak into the kitchen and grab food. He then will go sit literally in his closet and eat it. It's not always "bad for you" food. It's just food. I have three kids and I can't keep an eye on the fridge all 24 hours in the day. Paul has asked if we need to lock the pantry and fridge. I don't know if maybe that's going too far. I don't want to give him a complex either. I don't want him to have any bit of self loathing placed from us. He should know that we love him no matter what. But that's hard to do when you're literally wrestling food out of his hands. Today I started with a chart for his eating. He will put a sticker on the chart at breakfast, lunch, dinner and snack times. My only concern with this approach is that he's being "rewarded" for eating...maybe it's going to make it even worse...?? Why didn't these kids come with an instruction manual?? I'm just trying to do my best here and sometimes that just feels so totally inadequate it's not even funny.