In 2006, about three out of every 1,000 pregnancies of 28 weeks or more ended in stillbirth, and the rate has been inching down for decades, according to federal data.
To see how obesity impacted this risk, Yao and colleagues used records from Texas and Washington, which are among 17 states that collect pre-pregnancy weight data along with birth statistics.
The analysis found 9,030 stillbirths among 2.8 million single-child deliveries between 2003 and 2011.
About half of the women in the analysis were of normal weight; 26 percent were overweight; and the rest fell into four increasingly severe categories of obesity. Nearly 4 percent were morbidly obese, with a Body Mass Index (a ratio of height to weight) of 40 or more - or at least 235 pounds for a 5-foot, 4-inch woman.
Overall, the researchers found the stillbirth rate mirrored the national one - three in 1,000 births. But as the mother's weight and the fetal age increased, so did the risk of stillbirth. It doubled for moderately obese women, more than doubled with morbid obesity, and tripled with "super" obesity (a BMI of 50 or more).
At full term - between 37 and 42 weeks - the stillbirth risk for the most obese women skyrocketed. At 41 weeks, for example, a super-obese woman was almost 14 times more likely to have a stillbirth than a normal-weight woman. That's a more powerful link than previous studies have found.
"I don't think anybody expected to see so much increase in risk," Yao said.
Overall, obesity was associated with a quarter of the stillbirths that occurred at term, which "would make obesity the single most important risk factor ... in the general population," the researchers wrote.
Exactly why maternal fatness is harmful to the fetus is unclear, but it may involve insufficient oxygen, or hormonal or metabolic disturbances. Yao and his colleagues speculate that deterioration of the uterus or placenta plays a role.
At Drexel, he said, "we perform more routine ultrasounds and monitor fetal growth," and recommend delivery on the due date if an obese woman doesn't go into labor beforehand.
But there is no evidence that fetal surveillance reduces stillbirth, the researchers say in their study, published online last month in the American Journal of Obstetrics and Gynecology.
Urging women to lose weight before becoming pregnant is another prevention strategy.
"The preconception counseling part - we can probably do better," Yao said. "There are a lot of things women can do before pregnancy to reduce their risk. Unfortunately, that's not always part of the conversation."