Mothers who smoked or who did not take supplements correctly also were more likely to have babies who were underweight or born too early, the study found - and these factors seem to affect the foetus during the first three months of pregnancy, before a woman has had much prenatal care.
But early ultrasounds may help identify the babies most at risk, the study, published in the Journal of the American Medical Association, suggests.
Dr. Dennis Mook-Kanamori and colleagues at Erasmus Medical Center in Rotterdam studied 1,631 pregnant women, doing ultrasound scans
of their foetuses between 10 and 13 weeks gestation.
Babies that were the smallest during this period of early, rapid growth were also more likely to be born early or to be underweight at birth, Mook-Kanamori's team reported.
But as they grew into toddlers, these babies tended to grow too fast - a pattern that can cause such children to become obese
"Higher diastolic blood pressure and higher hematocrit levels were associated with a shorter crown to rump length," the researchers wrote. Hematocrit is a count of red blood cells in the blood.
A low hematocrit means anaemia, but levels can be too high if a person is dehydrated, smokes or has some kinds of heart disease
. The researchers suggested that if a woman was dehydrated, perhaps not enough blood was getting to the placenta to nourish the foetus.
Smokers and women who did not take folic acid supplements also tended to have small foetuses during the first trimester, the researchers found.
And these children, when born, grew at quicker than optimal rates. "Shorter first-trimester crown to rump length was associated with accelerated growth rates in early childhood," the researchers wrote.
"Complications of late pregnancy may, at least for some women, already be determined in the first 3 months post-conception, even before a woman has sought prenatal care," Dr. Gordon Smith of Britain's University of Cambridge wrote in a commentary.
"Combined ultrasonic and biochemical screening in early pregnancy may be able to identify women at high risk of complications in late pregnancy."