Data from over 5,000 individuals found that a measure of belly fat (waist:hip ratio) was associated with reduced cognitive function in older Irish adults (60+). Body mass index (BMI), however, was found to protect cognitive function.

BMI is a crude measure of body fat and cannot differentiate between fat and muscle — the muscle component is likely to be the protective factor.

Research indicates that as we age, our fat becomes less efficient at producing a hormone that helps support the growth and survival of neurons and helps regulate their activity.

That hormone is adiponectin, which is made by fat cells, circulates in our blood and enters our brain. Inside fat cells, its production is regulated by PPAR-γ (peroxisome proliferator-activated receptor gamma).

Adiponectin is anti-inflammatory and can help regulate neuronal activity, including turning activity of some neurons up and others down. However, adiponectin is reduced in Alzheimer’s patients. Delivering adiponectin to the brain has been shown to improve cognition in mice.

Chronic stress can also decrease fat's production of PPAR-γ and adiponectin.

Fat cells become less efficient at making adiponectin in obesity, and with age. One theory is that fat cells start making inflammation-promoting signals called cytokines and this inflammation then inhibits adiponectin production.

The shift from beneficial subcutaneous fat to unhealthy fat that piles up on our bellies and around the organs inside our abdominal cavity is one that naturally occurs with age, but it is of course worse if you have a lot of excess weight around your abdomen.

Genetic variations in PPAR-γ and adiponectin as well as low blood levels of adiponectin are associated with an increased Alzheimer's risk.

https://www.eurekalert.org/pub_releases/2018-08/tcd-mob080118.php