Yes. As the amount of fat in the body increases, so does the likelihood of developing certain cancers – those of the bowel (colon and rectum), kidney, gullet (oesophagus), pancreas, and gall bladder, and additionally in women, those of the breast (in postmenopausal women), lining of the womb (endometrium), and ovary.
Excess body fatness increases cancer risk most likely by promoting inflammation and increasing levels of a number of growth factors and hormones, which in turn promote the growth of cancer cells.
Although the risk is highest in obese people (e.g. colorectal cancer risk increases of 15% in overweight and of 32% in obese people, with a body mass index [BMI] of more than 30 kg/m2), the risk steadily increases with the amount of fat that people have. It is therefore recommended to aim for the lowest part of the healthy range that you can. This will obviously be different for different people depending on their build – so that a person with a slight build might aim towards the lower end of the range, and a more thickset (stocky) person might aim towards the middle or upper end of the range.
Some particularly muscular people, even though they do not have excess body fat, might find that they have a BMI in the “overweight” or even “obese” categories. However, the vast majority of people in these categories do have excess body fat.