A statistical comparison showed that every extra unit in body mass index (BMI, a height-to-weight ratio) in middle age corresponded to earlier onset of Alzheimer's by about 6.5 months -- what the authors termed a "robust" correlation.
"A healthy BMI at midlife may delay the onset of AD," the study paper said, referring to Alzheimer's disease.
Researchers used the recorded BMI of more than 1,300 Americans, all of whom were monitored for an average of 14 years after signing up to be studied.
The debilitating disorder is the most common form of dementia, which the World Health Organization (WHO) says affects nearly 50 million people worldwide -- some 7.7 million new cases per year.
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Being obese or overweight in middle age was known to increase the risk for Alzheimer's later, but it was not clear whether it affected the age of disease onset.
The WHO estimated more than 1.9 billion adults, of the world's total population of seven billion, were overweight in 2014. Thirteen percent were obese.
"We found that for every unit increase in body mass index when these individuals were 50 years of age, they developed Alzheimer's disease on average 6.5 months earlier," study lead author Madhav Thambisetty of the National Institute on Aging of the US health department's National Institutes of Health, said in a video recording.
People with a BMI of 25 and higher are generally classified as overweight, and 30 and over obese. In metric terms, it is calculated as your weight in kilogrammes divided by the square of your height in meters.
The average BMI of the study participants at 50 years was 25.8, said the authors. A "unit" increase would be one point, say from a BMI of 25 to 26.