Ever-growing waistlines could result in a big increase in the number of people who develop dementia in the future, researchers have warned.
Previous studies have shown that being overweight in middle age increases the odds of developing the mental disorder.
Data presented at the European Congress on Obesity suggests stemming the rise in obesity will cut dementia.
The Alzheimer's Society charity said regular exercise and a healthy weight were important for reducing risk.
Piling on too many pounds is known to be bad for the body, but there is growing evidence that it is also bad for the mind.
£940m saving predicted
Nobody knows exactly what causes dementias such as Alzheimer's disease, but body weight appears to be a risk factor.
One study of 8,500 Swedish twins showed that those with a body mass index (BMI) greater than 30, who are classified as obese, were almost four times as likely to develop dementia as those with a normal BMI.
Even those who were clinically overweight, a BMI between 25 and 30, were 71% more likely to develop dementia.
In England 24% of men and 26% of women are obese.
Researchers from the UK Health Forum used computer models to compare what would happen if obesity rates stayed the same or increased to 46% of men and 31% of women by 2050, which has been predicted by some groups.
They said rates of dementia would go from 4,894 cases in every 100,000 people over 65 to 6,662 cases in every 100,000 people over 65.
Keeping obesity levels constant would save around £940m in dementia care, the study predicted.
Tim Marsh of UK Health Forum said: "We've known for a long time about the risks to cardiovascular disease, stroke, cancer, type 2 diabetes, so this is a new concern.
"Obesity is a major concern that's going to have a major economic impact on the country and this further compounds that.
"The trouble is there's a 25-year lag in this. Obesity started increasing in the 80s."
Jessica Smith, a research officer at Alzheimer's Society, said: "It's easy to see the immediate impact of piling on the pounds, but we can't afford to ignore the long-term effects.
"Evidence shows that obesity increases the risk of developing dementia. This study highlights the impact obesity will have on the numbers of people with the condition in the future.
She added that "maintaining a healthy weight and exercising regularly - especially in midlife - are hugely important in reducing your risk".