The mice study from Georgia Regents University focused on a chemical called interleukin 1, a substance born from fat cells that can cause inflammation.
The obese mouse brains showed high levels of inflammation and low levels of a biochemical important to synapse function (synapses ensure messages travel efficiently between neurons). The substance was also found to be capable of passing the blood-brain
barrier, and seeped into the hippocampus area which is responsible for
memory and learning. This could explain why obese mice did poorly on mouse-sized cognitive tests.
Obviously, being obese doesn't automatically make you any less intelligent, but it might hamper your cognitive abilities. The upside is that you can reverse this just by losing weight through exercise.
When researchers put the obese mice were on a daily treadmill running regimen for three months, although they still weighed as much as their sedentary counterparts, they gained lean muscle and lost fat from their midsections. More importantly, they started performing better than the non-treadmill runners on cognitive tests because the signs of brain inflammation had been reduced.