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Headlines last week offered a glimmer of hope on obesity: A government study found that the obesity rate for children ages 2 to 5 dropped by about 40 percent between 2003 and 2012. That comports with another recent government report finding that, in several states, young, poor children are healthier.

This is encouraging but no reason for complacency. In fact, last week's announcement shows that obesity remains a daunting problem that demands more effort — from Americans and their government.

Assuming the results reflect a real and significant trend, what will happen when these children grow up? For Americans older than 5, obesity rates have stayed about the same in recent years. A third of adults are obese, and 17 percent of all children are morbidly overweight.

The positive spin on these findings is that Americans' waistlines have finally ceased to expand. We'd suggest that the country should not be comfortable that the ravages of obesity — diabetes, heart disease, hypertension, cancer and more — will diminish the living standards of merely a third of our countrymen, even if some of their children and grandchildren end up better off.

Meanwhile, maintaining even a diminished quality of life for overweight people is expensive. Researchers in 2012 estimated that keeping the obesity rate steady would save some $550 billion over the next two decades, compared to scenarios public-health experts feared. But that would still leave annual spending on treating obesity-related disease at about $150 billion a year.

The government should stop subsidizing crops such as corn, which gets converted into high-fructose corn syrup. It should conduct more research on what's behind the plateauing obesity rate and the improvement in toddlers. New labeling requirements for store-bought food, proposed last week by the Food and Drug Administration, will help. They will make it harder for food companies to confuse consumers with unrealistic serving sizes and will list added sugars, a major contributor to poor nutritional health. More difficult to implement, but probably more effective, would be direct financial incentives. Many public-health activists want to tax sugary drinks. Understandable, but studies and simple reasoning argue for taxing the underlying culprit, sugar, wherever it appears. A partial step would be to reform the food stamp program to promote healthier eating, as has already happened in a similar program.

All of the burden can't fall on government. Health insurers have begun to take a bigger role in encouraging physical activity and reasonable diets, including by adjusting premiums or other payments. They should continue looking for ways to reward people who improve their lifestyles. That could help insurers' bottom line — and the well-being of their customers.