Even overweight kids can be malnourished if they live on junk. Some foods that are usually thought of as junk food can still provide your children with the basic nutrients. Hot dogs are high in fat and salt. I wouldn't feed them to my child every day, but they do have meat protein in them. Same for hamburgers from fast food places.
Pizza is an excellent source of nutrition.
The cheese provides essential protein and fat while the crust provides carbohydrate calories. Maybe you can even sneak some vegetables onto the pizza. Some of the biggest feeding problems develop when parents push their kids to eat or to finish what's on their plate. The only healthy infant I ever saw who didn't gain weight was one whose mother was so anxious about his eating that she followed him around all day with food. When we finally convinced his mom to relax and leave him alone about food, he began to eat.