The results suggest that some previous studies, which have shown a strong link between childhood obesity and mental health, may not have fully accounted for family genetics and environmental factors. 

Children with obesity are more likely to be diagnosed with depression, anxiety, or attention-deficit hyperactivity disorder (ADHD). But the nature of the relationship between obesity and these mental health conditions is not clear. Obesity might contribute to mental health symptoms, or vice versa. Alternatively, a child's environment might contribute to both obesity and mood and behavioural disorders. 

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'Body mass index and childhood symptoms of depression, anxiety, and attention-deficit hyperactivity disorder: A within-family Mendelian randomization study' by Amanda Hughes et al. in eLife [open access]