Obesity rates in adolescence and young adulthood have increased in Sweden, reflecting global trends. To which extent this occurs across different socioeconomic strata has not been clarified. The aim of the present study was to investigate trends in social inequalities in body mass index (BMI) in young/mid-adulthood Swedish women. We obtained weight and height for all women aged 20–45 years, at their first registered pregnancy (< 12 weeks of gestation) in the Swedish Medical Birth Register 1982–2013 (1,022,330, mean age = 28.8 years), documenting education and county of residence. Trends in mean BMI and in the prevalence of BMI categories between 1982 and 2013 were estimated across education levels and geographical location. Overall, mean BMI increased from 22.7 kg/m2 (SD 3.2) to 24.3 kg/m2 (SD 4.4) between 1982 and 2013. Simultaneously, the prevalence of overweight and obesity (BMI ≥ 25 kg/m2) increased from 18.1 to 33.4% while that of moderate obesity (BMI ≥ 30 to < 35 kg/m2) and severe obesity (BMI ≥ 35 kg/m2) increased markedly from 3.4 and 0.4% to 7.4 and 3.1%, respectively. The prevalence of moderate and severe obesity more than doubled during the study period across all educational levels. In conclusion, BMI and moderate and severe obesity increased markedly among young/mid-adulthood Swedish women regardless of education with a widening gap between those with lower and higher education. These growing social inequalities in BMI are likely to cause a rising divide in serious health problems following early and long-lasting obesity.