Middle aged people who are overweight but not obese, are 71% more likely to develop dementia than those with a normal weight, according to research.
Previous studies have indicated a link between obesity and dementia.
But a study 8,534 of Swedish twins, in the journal Neurology, suggests just being overweight is also a risk factor.
About one out of every 20 people above the age of the 65 has dementia. The Alzheimer's Society said a healthy lifestyle could reduce the risk.
Those with a body mass index (BMI) - which measures weight relative to height - greater than 30, who are classified as obese, were 288% more likely to develop dementia than those with a BMI between 20 and 25, according to the study.
The clinically overweight, who have a BMI between 25 and 30, were 71% more likely.
Dr Weili Xu, from the Karolinska Institute in Stockholm, told the BBC: "We found in this study that being overweight is also a risk for dementia later in life."
"The risk is not as substantial as for [the] obese, but it has public health importance because of this large number of people worldwide who are overweight," Dr Xu added.
The study says 1.6 billion adults are overweight worldwide.
Alzheimer's Society head of research, Dr Susanne Sorensen, said: "This robust study adds to the large body of evidence which suggests that if you pile on the pounds in middle age, your chances of developing dementia later in life are also increased.
"By eating healthily and exercising regularly, you can lessen your risk of developing dementia."
Alzheimer's Research UK head of research, Dr Simon Ridley, said: "This study adds to existing evidence that excess weight in middle age could increase our risk of developing dementia.
"It's likely that dementia is caused by a complex mix of genetic, environmental and lifestyle factors. However, we still need to know much more about the causes of dementia if we are to find an effective treatment that is so desperately needed."