A US study appears to back previous research suggesting underweight babies are at a greater risk of depression.
Low birth weight is linked to a risk of poor health
Researchers found girls who had been born weighing under 2.5kg (5.5lb) were more prone to depression aged 13 to 16 than those born at a normal weight.
The Archives of General Psychiatry study, led by Duke University, examined data on more than 1,400 children, aged nine to 16.
They said further investigation was needed to pin down possible reasons.
Previous studies have said a potential for depression may lie dormant in small babies, before emerging later under stressful conditions.
The Duke University study found that among girls, 5.7% were born weighing less than 2.5kg, and of these 38% experienced depression at least once between the ages of 13 and 16.
This compared with 8.4% of those born at a normal weight.
On average, 23.5% of teenage girls with a low birth weight were depressed each year, compared with 3.4% of those born at a normal weight.
Regardless of their birth weight, no more than 4.9% of the boys experienced depression.
Low birth weight was not linked to an increased risk of any other psychiatric condition, including anxiety disorders, in either boys or girls.
The researchers' favoured theory for the link to depression is that the changes a foetus has to make to compensate for a harsh environment in the womb may in some way leave it poorly prepared for the conditions it will encounter in later life.
It is also possible that low birth weight is indicative of harsh living conditions, such as poverty, which may make a child experiencing them more likely to be depressed.
Alternatively, a depressed mother may be more likely to produce a child who is prone to depression - and to have a low birth weight baby because they may be more likely to smoke and drink during pregnancy.
However, the latest study found no evidence to support these later two ideas.
Writing in the journal, they said: "For the present, the findings suggest that paediatricians and parents of girls who were of low birth weight should pay close attention to their mental health as they enter puberty."
Maggie Blott, a consultant obstetrician at London's King's College Hospital, said there was evidence that babies who survived despite harsh conditions in the womb actually tended to thrive in the first months of life.
But she said it was much more difficult to pin down any long-term effect.
However, previous research has linked low birth weight to an increased risk of attention deficit disorder, as well as physical conditions such as cardiovascular disease, and diabetes.