Could it really be related? Midlife obesity has long been associated with increased risk of dementia, although the how the relationship works has been poorly understood. 

Researchers examined possible associations between cerebral brain volume and obesity in 733 middle age community adults. They found a significant association between visceral (abdominal) fat and low total brain volume. The authors suggest that inflammation resulting from fat cells may negatively impact brain tissue.

PositiveTip: Even if this isn't directly due to inflammation, there are many other great health reasons to maintain ideal weight.