The findings, published in the Lancet medical journal, suggest BMI was "positively associated" with 10 most common cancers, including uterus, cervix, thyroid, kidney, liver and colon.
Post-menopausal breast cancer and leukaemia were also a heightened risk, the scientists said.
A person is deemed to be overweight if they have a BMI score, calculated using their weight and height, of 25 to 30 and are obese if it is above 30.
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John Inge, the Bishop of Worcester, says the death of his wife from cancer at the age of 51 has set him in opposition to the legislation.
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