This was a " cross-sectional " study ( looking at data, from 473 individuals between ages of 20 -87, at one point in time ).
The volunteers were " cognitively healthy " ( using a test similar to an IQ test ) ; half were " lean " ( " normal " BMI ), half were overweight / obese.
Brain structures were analysed from MRI ( magnetic resonance imaging ) scans.
Our brains naturally shrink with age. The study found that " WHITE matter " ( part of the brain which transmits information ; white because of fatty protective protein called myelin ) was reduced - from middle age onwards - MORE in an overweight person, compared to a lean person. At 50 an overweight person had a comparable white matter volume to a lean person aged 60. GREY matter ( mainly nerve cell bodies ) was not affected here.
Association is NOT necessarily causation! The study authors couldn’t say whether obesity might cause the brain changes OR be the result of such changes. They couldn’t answer the question of whether the changes could be reversible with weight loss.
The study also found NO connection between being overweight / obese and " cognitive abilities ". In other words, such individuals were just as good at thinking, or ( like Arthur ) " participating on this site ( and ) tackling cryptic crosswords ".
Of course the world’s population is getting heavier, with well-known health consequences ( diabetes, cancers, heart disease ) - although life expectancy is also increasing. It seems that the health risks result, at least in part, indirectly - from raised blood pressure and lipids, and other effects. Such " metabolic " effects might include an inflammatory response in white matter of the brain ( suggested in the discussion part of this study ).
MUCH more work needs to be done before we have good evidence explaining a link between obesity and brain ageing. Meantime, of course, there are other reasons for avoiding obesity - or, at least, reducing it to being either overweight or lean. See " Fat Chance! " thread.