I also agree that snacking can be a good thing - if it's done with the right foods.
In Germany, snacking is fairly common. School children have a 10-20 minute break at school around 10am and the teachers encourage them to bring (healthy) snacks/sandwiches from home. At the office, 10am is usually "coffee break" and it's fairly common for someone to bring in treats (e.g. there is always someone with a birthday). My sister's team at work gathers every Friday to have a 10am "sausage breaks". And yes, they still eat lunch later.
A lot of people also have coffee and cake around 3-4pm, much like the English tea time. Especially on weekends, it's common for the family to gather for a piece of homemade cake, fruit bread or cookies. So, it's definitely not a US thing. I just think there is a problem with portion sizes and proliferation of fatty/sugary/chemically enhanced foods - and people don't know anymore what is "normal" food.
Anyway, this is way off topic
. Hope you're getting your son motivated for some activities!