> Scans show greater shrinkage in volume of white matter in overweight and obese people, although it does not appear to affect cognitive performance.

Perhaps this is a demonstration that the brain is over-engineered and the extra matter is insurance against damage. If the white matter is being lost slowly, the brain can continuously adapt asymptomatically.

There may come a point where there is so much loss/damage dementia is inevitable, implying obese people would have a higher long-term likelihood of dementia.

Edit: removed an off topic counter-reference.