In particular, they broke up BMI's into five groups: (1) 15-21.5, (2) 21.5-23.4, (3) 23.4-25.2, (4) 25.2-27.7, and (5) 27.7-45, where BMI's up to 25 are considered normal, up to 30 are considered overweight, and over 30 are considered obese. Even within the final group, not all the participants are obese.
It begs the question of why they didn't compare "normal" weight IQ's to "obese" weight IQ's, as this would be a big story and a more impressive research finding! It's likely that either they didn't have enough obese participants to satisfy statistical significance (so most of group (5) is actually individuals with BMI's of 27.7 to 30), or they didn't find that obese people had lower IQ's. When the BMI groups that they break up their data into as strange as this, and not at all the groups that are normally used in research papers, it begs the question of what kind of data massaging they had to do to find their conclusions. Did they try 100 different breakdowns of BMI groupings until they found one that (barely) satisfied statistical significance?
I remain skeptical as to the conclusions of this paper.