Americans, at least as a group, may have reached their peak of obesity, according to data the Centers for Disease Control and Prevention released Wednesday.

The numbers indicate that obesity rates have remained constant for at least five years among men and for closer to 10 years among women and children  long enough for experts to say the percentage of very overweight people has leveled off.

But the percentages have topped out at very high numbers. Nearly 34 percent of adults are obese, more than double the percentage 30 years ago. The share of obese children tripled during that time, to 17 percent.

“Right now we’ve halted the progress of the obesity epidemic,” said Dr. William H. Dietz, director of the division of nutrition, physical activity and obesity at the disease control centers. “The data are really promising.