It said a steep rise in obesity in the past 40 years may have increased cancer risk in younger generations.
And it warned the problem could set back recent progress on cancer.
The Society studied millions of health records from 1995 to 2014, publishing its findings in The Lancet Public Health.
In the last few decades, there has been mounting evidence that certain cancers can be linked to obesity.
‘Dangers of extra weight’
Researchers found that the rates of six out of 12 obesity-related cancers (colorectal, uterine, gallbladder, kidney, pancreatic and multiple myeloma – a blood cancer) all went up, particularly in people under the age of 50.
And they found steeper rises in successively younger generations aged 25 to 49 – and particularly in millennials, in their 20s and 30s.
For example, the risk of colorectal, uterine and gallbladder cancers has doubled for millennials compared to baby boomers, now aged 50 to 70, at the same age.
Some of these cancers increased in people over 50 too, but the rises were not as steep.
Researchers say this trend may be down to the rapid rise in obesity in the last few decades with “younger generations worldwide experiencing an earlier and longer exposure to the dangers of extra weight”.
Dr Ahmedin Jemal, from the American Cancer Society, said: “Our findings expose a recent change that could serve as a warning of an increased burden of obesity-related cancers to come in older adults.
“Most cancers occur in older adults, which means that as the young people in our study age, the burden of obesity-related cancer cases and deaths are likely to increase even more.”
Other risk factors
But the researchers could not explain why the rates of only half of the 12 obesity-related cancers had increased.
Meanwhile, they found cancers linked to smoking and infections were declining in younger age groups.
Dr Brenda Birmann, from Brigham and Women’s Hospital in Boston, told the Lancet Public Health that it was possible that risk factors other than obesity could play a part and this warranted further investigation.
“Importantly, the findings suggest the need for further close epidemiological monitoring of cancer incidence trends in younger adults,” she said.
Which cancers are caused by obesity?
According to the charity Cancer Research UK, obesity is the second biggest preventable cause of cancer in the UK, after smoking.
Research suggests bowel cancer, womb cancer, oesophageal (food pipe) cancer, cancer of the kidney, liver, upper stomach, gallbladder, ovarian, thyroid, meningioma (a type of brain tumour) and multiple myeloma (a type of blood cancer) and breast cancer in women after the menopause have all been linked to obesity.
Researchers say the risk increases as people get more overweight.
But of course, obesity is only one factor – the environment, genetics and other issues can also come into play. Not everyone who gets these cancers will be overweight and everyone who is obese will not necessarily get these cancers.
And scientists are clear that losing even small amounts of weight can help reduce the risk of cancer.
How does obesity lead to cancer?
Scientists still have a lot of questions to answer but there are currently three main theories about this.
Extra body fat does not just sit in the body doing nothing.
Fat cells help store energy, but they can also send chemical signals to other parts of the body. These signals may tell cells to divide more quickly, which can put people at risk of cancer.