Did you change your post? I'm editing to add that I agree to take the kids for a daily walk. To encourage your children to move and play and turn off/unplug the TV. My DD might fuss, but she finds something else to do. You need to find a way to allow your child to play and be an active little boy and not hold him hostage to the baby. The baby can learn to sleep with a normal amount of noise. Being active with his cousin is a good start! Maybe direct some of their play, like kicking a ball or playing on a playground or playing tag or catch.
You need to offer him only the food he needs to eat. I'm not into food fights with kids, but if my DD doesn't eat what's offered, then she's not then getting junk food. She gets to have healthy food later. I just matter of factly say this is dinner. Take it or leave it but I'm not making anything else. If we eat something she will not (like chili) I give her an alternative like low fat turkey slices, fruit, whole grain bread. Quick does not need to be junk food.
You also need to make the time for a family dinner, even if it's just you and your kids. Sit down and model the behavior you want from them. Eat with them. Enjoy the time. Talk about your day. Have a good experience that is more than just food. Studies have further shown that kids who eat with their families regularly are less likely to be in trouble. You are laying down foundations for his entire childhood - all the way to 18 and beyond. Parenting is a long haul, so keep your eye on the big picture vs the little ones. They cannot raise themselves. They NEED you to make the right choices FOR them at this age.
Your son could have been the boy I helped onto a swing months back. He was so big he couldn't breathe well, and he couldn't run and play with his siblings and friends at the playground. His grandmother couldn't lift him onto the swing and I barely could. The kid could not keep up with his peers. I felt so bad for him because he did want to play but was hampered by his size. Please change things for your family so your children are not left behind and suffer socially for something fixable.
Original post below:
Your pediatrician should be able to give you more info on proper diet, direct you to a nutritionist, etc. When I say "diet" I mean "type of food consumed" not "calorie restriction". And just like adults, if he eats a lot and does not move, then that needs to be changed. If you have been told to change the foods he eats or how much he eats, then you stick to it by being firm. "This is what is for dinner. If you not eat, you can get down, but there is no snacking" or offer him a healthy snack only, like a toddler-sized portion of fruit. It may also be that the entire family needs to adapt. He will be more likely to eat fruit, veg, lean meats, etc. if he sees everyone else doing so.