Do we need a study to evaluate this? Apparently so. And, yes! Overweight children are 18% more likely to have lower extremity injuries compared to normal weight children. The risk increases to 24% in obese children and 34% more likely in extremely obese children. Good news is that obese children are not at increased risk of upper extremity injuries.
The recommendations should be to discourage obesity in children. Good diets. Healthy snacks. Exercise daily.
Hope this helps.