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The proportion has been broadly static for more than a decade at about 21% to 23%, the latest NHS statistics show.
“There is continued concern over the levels of overweight and obesity among children in Scotland,” the health service said.
“Obesity during childhood is a health concern in itself but can also lead to physical and mental health problems in later life, such as heart disease, diabetes, osteoarthritis, back pain, increased risk of certain cancers, low self-esteem and depression.”
There was a slight increase in the level of children classed as a healthy weight, up from 76.9% to 77.5% in a year.
The latest figures, from 2012-13, show that 21.3% were “at risk” of being overweight or obese, down slightly from 21.9%.
Sports minister Shona Robison said: “This is a small but encouraging move in the right direction, with more primary one children classed as healthy weight than last year.
“A key focus of our action to cut obesity is to focus on early years, where evidence suggests the greatest impact can be made.
“We are supporting child healthy weight interventions and are increasing opportunities for children to get involved in sport and physical activity, through active schools and our target of all primary children having two hours of PE lessons a week.”