Cancer deaths are dropping overall, but not the ones linked to obesity.

That’s what mounting evidence now shows. A sweeping new report on U.S. cancer trends revealed that cancers linked to obesity are becoming more common. Another study, presented in July at the Endocrine Society Annual Meeting in San Francisco, found that deaths from obesity-related cancers have more than tripled over the past two decades.

These include esophageal, colon and rectal, breast (postmenopausal), uterine, gallbladder, upper stomach, kidney, liver, ovarian, pancreatic, thyroid, meningioma (brain), and multiple myeloma — 13 types in all, now accounting for 40% of new cancer diagnoses in the U.S. Women, older adults, Native Americans, and Black Americans are especially vulnerable.

Second only to smoking, obesity ranks as one of the leading preventable causes of cancer. Yet even as the public’s awareness of smoking’s risks has dramatically increased, experts warn we’ve underestimated just how much excess weight — and the complex biology behind it — can fuel the disease. What exactly drives this link is not fully understood, but experts are homing in on some strong possibilities. It could be estrogen, fat cells, the microbiome, insulin resistance, or all of the above. One thing is sure: The public health threat of obesity is only increasing.

So what does this mean for cancer prevention, and how can you protect yourself? Behind the drop in overall cancer rates are significant declines in the number of smokers — and smoking-related cancers. Between 1965 and 2015, the smoking rate fell from 42% of the population to 15%, putting a major dent in rates of lung cancer, which is still the deadliest form. Meanwhile, obesity rates have gone the other way, rising from 13% in 1960 to more than 40% today.

Estimates reveal a crucial gender difference. While overall cancer diagnoses in men are down —decreasing from 2001 through 2013, and plateauing after that — the same is not true for women, according to the April report, jointly published by top health organizations like the CDC, the National Cancer Institute, the American Cancer Society.