The researchers analysed measurements from 22,421 women born in Sweden between 1973-1988 taken at an average age of 26 years.
Forty-two percent of the women's mothers had reported at their first antenatal visit (about 10-12 weeks into their pregnancy) that they smoked.
Lead author Dr Jose Derraik, a senior research fellow from the Liggins Institute, said it appeared the chemicals in cigarettes may turn on or off the genes involved in controlling growth.
"When a woman smokes during pregnancy, chemicals from the cigarettes travel through her bloodstream across the placenta and then to the baby, permanently changing the way the baby's body uses and stores energy," he said.
"Some of these chemicals can interfere with growth, which probably explains why babies born to mothers who smoked during pregnancy are often smaller."
The risk of obesity was higher in daughters of mothers who were heavier smokers, compared to those who smoked fewer than 10 cigarettes a day.
US research found smoking during pregnancy made babies better at forming fat cells.
"This would be useful in helping a small baby grow faster, but it would also explain, at least in part, why they have a greater risk of obesity later in life," Derraik said.
Data pulled together in 2016 from many studies identified nearly 3000 genes whose activity appeared to be affected in babies whose mothers smoked during pregnancy.
One of the studies other authors, Professor Wayne Cutfield, said stopping smoking before pregnancy also reduced the risk of pregnancy complications, birth defects, miscarriage, low birth weight and asthma in their children.