PubMed: Aerobic fitness improves academic performance in 4th to 8th grade students

"Aerobic fitness was a significant predictor of academic performance; weight status was not. Although decreasing BMI for an overweight or obese child undoubtedly improves overall health, results indicated all students benefit academically from being aerobically fit regardless of weight or free/reduced lunch status. Therefore, to improve academic performance, school systems should focus on the aerobic fitness of every student."

Evidence that aerobic fitness is more salient than weight status in predicting standardized math and reading outcomes in fourth- through eighth-grade students.