Carrying extra weight boosts the risk of tumours of the bowel, kidney, pancreas and ovary, researchers found.
Shedding the pounds helped reduce the chances, and even more so if people also had heart disease, they said.
Dr Helen Corker, of the World Cancer Research Fund, said: “We already know that obesity is an important risk factor for cancer.
“But these striking findings show that the risk differs depending on whether people also have cardiovascular disease.
“Maintaining a healthy weight can offer even greater benefits for particular groups.”
Around a quarter of English adults are obese, with a further 38 per cent overweight but not obese.
Worldwide, experts predict one billion people will be obese by the end of the decade.
Research has shown overweight people cost the NHS an extra £13.7billion a year.
Obesity is linked with a range of deadly conditions, including heart disease, stroke, diabetes and various forms of cancer.
Having a body mass index (BMI) of more than 25 — meaning you are overweight — increases the risk of at least 13 types of cancer.
These include breast cancer in postmenopausal women, bowel, liver, kidney, pancreatic and ovarian cancers.
The latest study, published in BMC Medicine, looked at how people’s weight impacted their risk of the disease, particularly if they already have heart disease or diabetes as well.
Researchers tracked health data from more than 577,000 adults in Britain and other European countries for an average of around 11 years.
More than 52,000 developed cancer over the course of the study.
Overall, people with higher BMIs were found to be a tenth more likely to get obesity-related cancers even if they didn’t have heart disease or diabetes.
For people with either condition, every five-point increase in BMI boosted the risks of cancer by 11 per cent.
The chances were especially high for people who were both obese and had heart disease, so they would benefit most from losing weight, researchers said.
Dr Heinz Freisling, of the International Agency for Research on Cancer, said: “For so long, research has focused solely on how BMI affects cancer risk for the general population.
“However this study has separated the risks for people with cardiovascular diseases — further showing the risk that living with overweight and obesity can have on cancer.
“This is a step in the right direction, but more research needs to be done to help provide further useful insights into how body weight influences cancer risk.”