"Coloured, white, and Indian women follow closely, with around a quarter being obese," the institute's South Africa Survey shows.
In contrast, 18% of all white men are obese, followed by 9% of Indian, 8% coloured, and 6% of black men.
The figures were obtained from the SA Medical Research Council and are based on Body Mass Index (BMI), calculated using a person's weight and height.
A person is obese if their BMI exceeds 30.
The SAIRR said: "According to the World Health Organisation (WHO) obesity was previously associated with high-income countries, but is gaining prevalence in low- and middle-income countries."
In October 2011 Compass Group Southern Africa, a food services company, placed South Africa third in the world in obesity rankings, after the United States and Great Britain.
Lerato Moloi of the institute's research department said: "Obesity is linked to a number of lifestyle diseases such as diabetes and heart disease, both of which are among the top 10 causes of death in South Africa."
Between 2004 and 2009 the numbers of people who died from diabetes and certain forms of heart disease increased 21% and 11% respectively, according to data contained in the institute's survey.
The WHO estimates that globally approximately 2.8m people die every year as a result of being overweight or obese.
Last week Linda Fried, dean of the Mailman School of Public Health at Columbia, told the World Economic Forum at Davos that in another 20 years, between 50% and 60% percent of the world's population could be overweight.
Source: Sapa via I-Net Bridge
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