The average UK birth weight is 3.3kg (7lb 5oz)
Further evidence has emerged that babies who are small at birth are more likely to start puberty early.
Rapid weight gain in the first two years of life is also associated with earlier onset of puberty, the American Journal of Clinical Nutrition reports.
The reason for the link, which was apparent in boys and girls, is not yet clear, the German researchers said.
Early puberty has been associated with an increased risk of breast and testicular cancer.
It has also been linked to other hormonal changes that could play a role in cancer's development.
The World Cancer Research Fund who backed the study said better understanding of factors early in life which increase future risk of cancer could potentially help develop strategies to prevent the disease in the first place.
It is not the first time factors such as low birth weight have been linked with early puberty.
But previous studies have focused solely on girls and used first period as a measure of the start of puberty.
In the latest study, researchers looked at a sample of 215 boys and girls who had height and weight measured regularly from birth to early adulthood.
They calculated when children had the growth spurt that pre-empts puberty.
Those born at 2.5kg-3kg (5.5lbs-6.6lbs) started puberty seven months earlier than heavier babies.
And those who grew fastest as infants tended to have their puberty growth spurt four months earlier.
The study did also show that for girls, rapid early weight gain was also related to starting their periods earlier.
Study leader Professor Anja Kroke said: "More studies are now needed to identify the physiological mechanisms by which a low birth weight and rapid early weight gain affect the timing of the pubertal growth spurt.
"In addition, by gaining a better understanding of why early puberty increases cancer risk, we can improve our understanding of the causes of cancer, and therefore raises the possibility of preventing future cancer cases."
Dr Panagiota Mitrou, science programme manager for the WCRF, said: "This study shows that what happens to us even in the womb can influence risk factors for diseases much later in life.
"Until more research is done, the best advice for parents is to give their children a healthy start in life by encouraging them to get into the habit of eating a healthy plant-based diet, be physically active and maintain a healthy weight."
Professor Fran Ebling, an expert in regulation of puberty and weight at the University of Nottingham, said these sorts of studies were very hard to do so the results were very impressive.
"This points to what we had thought - that babies who are born smaller and who put on weight more rapidly start puberty earlier.
"But what is controversial is they don't find a link between birth weight, early puberty and childhood obesity - and there are other studies that have found that."