Being overweight is a risk factor for cancer
The study, which looked at 45,000 cases of cancer in 1m women over seven years, says this is about 5% of such cases.
It is published online by the British Medical Journal and blames excess fat for 50% of cases of womb cancer and a type of oesophageal cancer.
Last week an international study warned of the link between cancer and weight.
The World Cancer Research Fund warned that carrying excess weight significantly increased the risk of cancer.
Figures indicate that about 23% of all women in England are obese and 34% are overweight.
The latest study looked at how often cancers occurred in 1.2m UK women aged 50 to 64 over a seven year period. More than 45,000 cases of cancer and 17,000 cancer deaths occurred during that time.
Lead researcher Dr Gillian Reeves, from Oxford University, said:
"We estimate that being overweight or obese accounts for around 6,000 out of a total 120,000 new cases of cancer each year among middle-aged and older women in the UK.
"Our research also shows that being overweight has a much bigger impact on the risk of some cancers than others.
"Two thirds of the additional 6,000 cancers each year due to overweight or obesity would be cancers of the womb or breast."
The research found that the link between weight and risk of cancer depended on a woman's stage of life.
For example, being overweight increases the risk of breast cancer only after the menopause and the risk of bowel cancer only before the menopause.
Sara Hiom, from Cancer Research UK, said: "This research adds to the evidence regarding the impact of being overweight or obese on developing cancer and dying from the disease.
"While most people readily associate carrying extra weight with being a general health risk, many do not make a specific link with cancer."
Dr Ian Campbell, medical director of the charity Weight Concern, said: "Whereas it was once thought there was little one could do to prevent cancer, it's now clear that lifestyle impacts greatly on overall cancer risk."The message is clear. Invest in a healthier lifestyle today and we can reap the benefits of reduced disease risk and longer life tomorrow."