Yes, you can influence your child’s weight during pregnancy. A study done in Finland showed that a maternal weight gain of more than 7 kg (or 15.4 pounds) in the first 20 weeks of gestation predicts overweight/obesity (using BMI) and abdominal obesity in adolescence. However, an even stronger predictor of adolescent overweight/obesity and abdominal obesity was maternal obesity before pregnancy.
If you fall in this category, and you want your children to be as healthy as possible, not all hope is lost. Please see the post on how lifestyle behaviors can change those children that have predetermined obesity risks.
Source: Laitinen J, et al, Maternal weight gain during the first half of pregnancy and offspring obesity at 16 years: a prospective cohort study, 2012 May;119(6):716-23. doi: 10.1111/j.1471-0528.2012.03319.x.