Los Angeles ? They say that what goes up must come down. But in the U.S., some trends seem to go in only one direction. For instance, the number of Americans who are overweight or obese just keeps growing. As the population ages, so does the number of older people suffering from Alzheimer’s disease and other forms of dementia.

Could there be a connection?

Possibly, according to a study published Wednesday in the Journal of the American Geriatric Society.

Researchers from Northwestern University’s Feinberg School of Medicine and colleagues around the country examined data from the Women’s Health Initiative. They focused on 8,745 volunteers who participated in clinical trials of hormone replacement therapy and were at least 65 years old.

For this cohort, data were available on their height and weight (and thus their body mass index), as well as their cognitive function (as measured by a test called the Modified Mini-Mental State Examination, aka 3MSE).

Overall, the researchers found that the higher one’s BMI, the lower her score on the 3MSE test. For every additional point on the BMI scale, test scores fell by nearly 1 point. (A 5-foot-6 woman would have to gain 6 pounds to increase her BMI by one point.) The researchers theorized that the circulation problems and inflammation brought on by obesity cause damage to the brain, resulting in dementia.

After adjusting for each woman’s age and level of education, the average test score of those who had a healthy weight (BMI less than 25) was 95.2, while the average test score of those who were heaviest (BMI greater than 40) was 94.1. The overall trend was statistically significant.

But on further analysis, that wasn’t true for everyone. Among the 25 percent of women with the highest ratio of waist size to hip size, test scores rose along with BMI.