WASHINGTON — Rates of adult obesity increased in six U.S. states and fell in none last year, and in more states than ever – 20 – at least 30 percent of adults are obese, according to an analysis released on Thursday.

The conclusions were reported by the Trust for America’s Health and the Robert Wood Johnson Foundation and were based on federal government data. They suggest the problem may be worsening despite widespread publicity about the nation’s obesity epidemic, from First Lady Michelle Obama and many others, plus countless programs to address it.

From 2011 to 2012, by comparison, the rate of obesity increased in only one state.

The 2013 adult obesity rate exceeds 20 percent in every state, while 42 have rates above 25 percent. For the first time two states, Mississippi and West Virginia, rose above 35 percent. The year before, 13 states were above 30 percent and 41 had rates of at least 25 percent.

Adult obesity rates increased last year in Alaska, Delaware, Idaho, New Jersey, Tennessee and Wyoming.

Nationally, rates of obesity remained at about one-third of the adult population, according to The State of Obesity: Better Policies for a Healthier America (stateofobesity.org), while just over two-thirds are overweight or worse.

Rates of childhood obesity have leveled off, with about one in three 2- to 19-year-olds overweight or obese in 2012, comparable to rates over the last decade.

Continuing a years-long trend, nine of the 10 states with the highest rates of obesity are in the South. The West and Northeast had the healthiest BMIs, with Colorado boasting the lowest adult obesity rate, 21.3 percent.

Obesity also tracked demographics, with higher rates correlating with poverty, which is associated with lower availability of healthy foods and fewer safe neighborhoods where people can walk and children can play for exercise. For instance, more than 75 percent of African Americans are overweight or obese, compared with 67.2 percent of whites.

That pattern affects children, too. In 2012, just over 8 percent of African American children ages 2 to 19 were severely obese, with a BMI above 40, compared with 3.9 percent of white children. About 38 percent of African American children live below the poverty line, while 12 percent  of white children do.

“Obesity rates are unacceptably high, and the disparities in rates are profoundly troubling,” said Jeffrey Levi, executive director of TFAH.