Re: Zone/Paleo and a young teen (13)
I wouldn't restrict him eating milk and dairy (unless he is lactose intolerant) at his age, especially if he hasn't gone through puberty. As you no doubt know most children who have a little extra weight will naturally shed it as they grow, make sure he knows this too.
I would echo the comments on food education. Teach him what is healthy, how to make good food choices, and how to read nutritional labels.
Don't restrict calories in any way (including the zone diet).
Teach him about sugar but there is nothing wrong with him enjoying some unhealthy food/drink once in a while, again especially at his age. If he is very motivated reduce the consumption to once a week. It may help with his skin when he goes through puberty proper, and which can be a significant source of frustration for a lot of teenagers.
Up the meat intake!