713 people in this study had dementia. 354 were overweight, 359 were normal or underweight. Don't see the weight connection here.

Fat, Flabby and Forgetful?
John Luik, TCS Original Article

They're back! Not long after the furor caused by the Centers for Disease Control's revised "figures" which showed that not 400,000 but about 26,000 Americans died annually from obesity and that being overweight might well be protective against premature death, the fat police are at it again with their scary headlines about the dangers of fat. This time the story is perhaps even more dramatic since it is about how middle age obesity "causes" late life dementia. So the supposedly bad news isn't just that being fat will likely kill you before you reach old age, it's also that if by some chance you do survive an early death you can worry about spending your golden years crazy.