To investigate the association between maternal early pregnancy body mass index (BMI) and offspring sleep apnea diagnosis. We conducted a nationwide cohort study among 3,281,803 singleton live births in Sweden born 1983-2015. Using national registers with prospectively recorded information, we followed participants for a sleep apnea diagnosis from 2 to up to 35 years of age. We compared sleep apnea risks by early pregnancy BMI categories using hazard ratios (HR) with 95% confidence intervals (CI) from adjusted Cox models. To address confounding by factors shared within families, we conducted sibling-controlled analyses and studied the relation of siblings' maternal BMI with index offspring's sleep apnea risk. There were 17,830 sleep apnea diagnoses. Maternal early pregnancy BMI was positively associated with offspring sleep apnea risk; compared with women with normal BMI (18.5-24.9), adjusted HR (95% CI) of offspring sleep apnea for maternal BMI categories 25.0-29.9 (overweight), 30.0-34.9 (obesity class I), and ≥35.0 (obesity class II or III) were, respectively, 1.14 (1.09, 1.19), 1.28 (1.20, 1.36), and 1.40 (1.27, 1.54). Corresponding HR from sibling-controlled analyses representing risk change for maternal BMI differences between pregnancies were, respectively, 1.13 (1.01, 1.26), 1.17 (0.97, 1.42), and 1.32 (0.97, 1.80). HR by siblings' maternal BMI were attenuated, suggesting a weak role for shared familial factors. Other pregnancy, birth, and neonatal complications were associated with offspring sleep apnea risk, but did not substantially mediate the association with maternal obesity. Maternal overweight and obesity are associated with offspring sleep apnea risk in a dose-response manner.