Controlling each person's individual diet would be incredibly time and resource consuming while infringing on the person's rights. It would be nearly impossible to fully regulate individual diets as each person's dietary needs vary greatly. A decent alternative would be to provide tax or healthcare benefits to those that keep a healthy lifestyle.
No, the government should not regulate an individual's diet because what a person puts into his body is a basic human right. Individuals who make poor diet choices pay the price in many ways, both through increased health-care costs and diminished physical abilities. The government is not affected by an individual's diet, so the government has no right to regulate that diet.
Adults should be permitted to make their own dietary decisions. The government should not be permitted to regulate the diets of competent adults or of children who are supervised by competent adults. The government should have a role in overseeing the safety of food and in providing accurate information on the nutritional values of different consumables.
It is neither the government's responsibility nor place to regulate individual diets. People should not be policed over something as tedious as food. As citizens of a free nation, people have the right to choose what goes into their bodies, whether or not it is healthy. Ultimately, however, people should be responsible for the consequences of what they choose to consume.