The obesity rate among low-income children between the ages of 2 and 4 is falling in 19 U.S. states and territories after having doubled in the past 30 years, a report released Tuesday shows.

Although the declines were small in most cases, officials from the U.S. Centers for Disease Control and Prevention said they were a sign of progress.

“It’s encouraging news but we’re very, very far from being out of the woods,” CDC Director Tom Frieden said on a call with reporters. “The fight is far from over.”

Obesity rates fell by more than 1 percentage point in Florida, Georgia, Missouri, New Jersey, South Dakota and the U.S. Virgin Islands from 2008 to 2011, and by smaller amounts in 13 other states.

In 21 states and territories there was no significant change in obesity prevalence, and three states saw obesity rates tick slightly upward in the years under review.

Between 1976 and 1980, the obesity rate among children 2 to 5 years old was 5 percent, compared to 12.1 percent from 2009 to 2010.

The study included 12 million children from 40 states, Washington, D.C., the U.S. Virgin Islands and Puerto Rico. Researchers measured their height and weight between 2008 and 2011 to calculate body mass index. Most of the children were participants in the Special Supplemental Nutrition Program for Women, Infants and Children, which provides federal assistance to states for low-income mothers.

Ten states - Texas, Oklahoma, Louisiana, South Carolina, Virginia, Delaware, Wyoming, Utah and Maine - did not participate in the CDC study because they either did not have consistent data between 2008 and 2011, or they changed their methodology, which could have affected results, the CDC said.

About one in eight preschoolers - 12.5 percent - in the United States is considered obese, and these children are five times more likely to be obese as an adult. Obesity rates are higher among black (one in five) and Hispanic children (one in six).

The news drew the attention of first lady Michelle Obama, who developed the “Let’s Move!” campaign to combat childhood obesity.

“While this announcement reflects important progress, we also know there is tremendous work still to be done to support healthy futures for all our children,” she said in a statement.

CDC officials said they hope the Affordable Care Act, President Barack Obama’s healthcare reform law that requires most Americans obtain insurance by 2014 or pay a fine, will help rates continue to decrease because obesity screening is covered under the law by most private insurance plans.

Childhood obesity often leads to other health complications, including High cholesterol, high blood sugar, asthma and mental health problems, the CDC said.

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By Yasmeen Abutaleb