I teach high school. Teenaged boys (most, at least) eat nonstop. They sit in class when they are supposed to be working talking about food. One pair of boys, this year, has had the same conversation about sandwiches about a dozen times. Several years back, I had two boys in class that talked about what they watched on the cooking channel like it was porn.
When I lived with my older teenaged brother, my mom had to give me food to hide in my room so my brother would not find it and eat it. My parents did discover was that if it took a long time to prepare, it was less likely to disappear....So meat stayed frozen, as did pasta sauce, etc. "Good Dinners" consisted of small roasts (take an hour roast), rather than steaks that can be broiled in ten minutes. My brother was capable of eating two pounds of deli meat in a less than five minutes. There was always plenty of popcorn we could pop, a can of soup we could open, or the ever present Top Ramen.
And there was never soda in our house, not even juice (liquid candy, essentially). Water was fine, and if we wanted it flavored, there was unsweetened koolaid that we had to make (and mix in the sugar) ourselves.
What finally solved the problem was when my brother went to work at a restaurant that provided a full meal (and all the soda he could drink) for the shift. It was a match made in heaven. Your son is 16. Send him to work at a pasta restaurant. Make him eat there and fill up. He will also probably be working during the dinner hour, so it kills two roast chickens with one stone....
Good Luck!
Shoshana