WASHINGTON — Prevention efforts are starting to yield results in the battle against obesity, but rates still remain high, according to “F as in Fat: How Obesity Threatens America’s Future 2013.”

The study, conducted by the Trust for America’s Health (T.F.A.H.) and the Robert Wood Johnson Foundation (R.W.J.F.), found that after three decades of increases, adult obesity rates held steady in every state except one, Arkansas.

“While stable rates of adult obesity may signal prevention efforts are starting to yield some results, the rates remain extremely high,” said Jeffrey Levi, Ph.D., executive director of the T.F.A.H. “Even if the nation holds steady at the current rates, baby boomers — who are aging into obesity-related illnesses — and the rapidly rising numbers of extremely obese Americans are already translating into a cost crisis for the health care system and Medicare.”

During 2012, the rate of adult obesity exceeded 30% in 13 states, while 41 states had rates of at least 25%. Every state was above 20% during 2012.

As recently as 1991, no state had an obesity rate of more than 20%, and in 2000 no state was above 25%. In 1980, the national average of obese adults was 15%.

For adult obesity rates, Mississippi, which had been the worst rated state for the past eight years, gave up its title to Louisiana, which finished at 34.7% (compared with 34.6% for Mississippi). Other states exceeding the 30% rate were Arkansas (34.5%), West Virginia (33.8%), Alabama (33%), Oklahoma (32.2%), South Carolina (31.6%), Indiana (31.4%), Kentucky (31.3%), Tennessee (31.1%), Michigan (31.1%), Iowa (30.4%) and Ohio (30.1%).

Of the states with the 20 highest adult obesity rates, only Pennsylvania is not in the South or Midwest.

Colorado once again was the best, coming in at 20.5%, which was down from 20.7% in 2011 and compared with 19.8% in 2010, when Colorado was the only state with a rate below 20%.

This year’s report examined how obesity rates vary by age, gender, education and income.

In looking at age, the obesity rates for baby boomers (ages 45 to 64), reached 40% in two states (Alabama and Louisiana) during 2012 and were 30% or higher in 41 states. By comparison, obesity rates for individuals over the age of 65 exceeded 30% in only one state (Louisiana), and obesity rates for young adults (ages 18 to 25) were below 28% in every state.

The report also found that obesity rates by gender are now consistent. The obesity rate for men was 35.8% in 2012, and for women it was 35.5%. The findings mark a change from 10 years ago when the rate for men was approximately 6 percentage points lower (27.5% versus 33.4%).