After smoking and poor diet, obesity is currently estimated to be the third most prevalent factor associated with 'preventable' cancers.

Some studies have quantified the increased risk at somewhere around 15% ( example ref.)

The mechanisms by which obesity may increase the risk of cancer are not well understood, but it is believed that the combined effects of the adipose tissue environment and the endocrine alterations that accompany it among obese people both interact to promote tumor initiation and progression.

Source Wikipedia

In particular, it's suggested that obesity may be acting as a persistent low-level 'inflammation' which could lead to DNA damage, and then on to cancer.