A study from the Harvard School of Public Health found that mothers who gained weight between pregnancies face a much greater risk of complications the second time around. The study of 150,000 Swedish women found that those who gained 3 or more units of body mass index (BMI) - compared to those who gained 1 or less - had a 78% greater chance of pre-eclampsia, 76% greater chance of gestational hypertension, and a bit more than twice the chance of gestational diabetes. Odds for Caesarean delivery and stillbirth were significantly greater.
Let's break it down a bit - to increase her BMI by 3 units, a 5-foot-5-inch woman weighing 125 lbs (BMI = 20.8) would need to gain 18 pounds. She would still fall within normal range, but would have much higher risk of complications with the second pregnancy.
Even modest increases in BMI before pregnancy could result in complications, even without the woman becoming overweight.