The sample size in this BMJ reported study isn’t big enough for reliability but the findings are intuitively right in my book:

“In 1999, 43% of the population had a BMI that put them in the overweight or obese range, of whom 81% perceived themselves to be overweight or very overweight. In 2007, 53% of the population had a BMI in the overweight or obese range, of whom only 75% reported themselves to be overweight, very overweight, or obese.”