As a parent, you have many obligations and responsibilities to juggle, all centered on your kids. You constantly serve as an example, not just when they are little, but throughout their lives. These obligations and burdens mean that you are a constant role model; you are the person that your kids look up to.
This means that how you take care of yourself will have an impact in shaping your children's health over the course of their lives, too. If you are overweight, and do not take the time to exercise and manage your health, how can you expect your children to do so? If you see exercise as a chore or a burden, how long before your kids pick up that attitude from you and carry it forward throughout their lives?
Obesity is something that is determined in part by genetics, but is mediated by several other factors as well, among them diet, exercise, and activity level. Kids are, by nature, high energy. They are always running and shrieking when they are little, and burn off lots of energy by playing.
Make that your focus. Take the time to play with them. Do not make exercise 'trudge on the treadmill'. Make it, "OK, let's go to the park and play ultimate Frisbee". Do things together as a family. Plan family hikes, walks, and bike rides. Use them as an excuse to get some exercise together and talk about the day.
How much exercise is enough? In general, try to get 30 to 60 minutes of low-level exercise per day, whether it is walking through the park at a brisk pace, running with the dog, or chasing your kids around the playground with a super soaker. Whatever you do, make it fun.
Give your kids some input into what activities you will do as a family. Some kids get into competition and sports, while some would rather do something fun that does not involve proving that they are better than anyone else. In particular, pay attention to your introverted children and let them know that what they want to do matters and that they will not get bullied by their older, more assertive siblings.
Since your kids will learn from your example, make sure you are setting the right one. If you are not taking the time to run around and play, they will emulate you and, once a child becomes obese, they can get 'stuck' in that health problem for the rest of their lives.