I think they are guilty of neglect. Children, particularly when small, only have access to the food that their parents provide for them. Therefore, if a child is obese, in most cases this can only be as a result of the parents giving the child too much too eat. Since all medical evidence suggests obesity is very damaging to a child's health, this can only be child neglect.
There are of course varying levels of neglect. Failure to feed your children would be the most egregious example of neglect, but overfeeding your children to the point of obesity is neglect as well. Such parents are neglecting their responsibility to shepherd their children into adulthood with some chance of living a healthy life. Children do not control the purse strings in a family. They do not get to decide what foods are bought at the grocery store. If parents have such a difficult time telling their children 'no' when it comes to unhealthy eating, at the very least they can refrain from buying the unhealthy foods to begin with.
The parents of obese kids should be held accountable and could be charged with neglect. Especially when the kids are such a young age, the parents have great control over what foods they eat. They should eat more fresh food and whole grains and eat at less fast food places.
I definitely think that the parents of obese children are guilty of neglect. Kids cannot choose for themselves what they want to it unless an adult allows it. That responsibility should be up to the parent in regards to a child's diet. A child should have to adhere to what his or her parents want them to have as a diet.
Parents of obese children are not necessarily guilty of neglect. While the quantity and quality of the food given to a child is an important factor in obesity, there are other factors. There are genetic factors which are beyond a parents control that could cause obesity. Also once a child is a certain age, they have the independence to eat different foods at school or a friends house.