Children in England and Scotland were more likely to be overweight or obese than those in Northern Ireland or Wales. Those in disadvantaged areas of England and Scotland were more likely to be overweight.
Ethnic groupings also made a difference. While only 9% of Indian 3 year olds were obese or overweight, the problem affected 23% of white children and 33% of black Caribbeans.
The research was carried out using data from the Millennium Cohort Study, which is tracking children born in the UK between 2000 and 2002.
Professor Heather Joshi, of the Centre for Longitudinal Studies, which helped carry out the research, said the findings showed obesity had to be tackled early.