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Importance: Prenatal experiences can influence fetal brain development., Objective: To examine associations of maternal prenatal body mass index (BMI) with cognition and behavior of offspring born full-term., Design, Setting, and Participants: This cohort study examined follow-up data from a breastfeeding promotion intervention at 31 hospitals and affiliated polyclinics in the Republic of Belarus. Participants included 11 276 children who were evaluated from birth (1996-1997) to adolescence (2017-2019), with maternal BMI information available in prenatal medical records., Exposures: Maternal BMI, calculated as weight in kilograms divided by height in meters squared, after 35 weeks gestation; secondary analyses examined maternal BMI at other time points and paternal BMI., Main Outcomes and Measures: Trained pediatricians assessed child cognition with the Wechsler Abbreviated Scales of Intelligence (WASI) at 6.5 years and the computerized self-administered NeuroTrax battery at 16 years, both with an approximate mean (SD) of 100 (15). Parents and teachers rated behaviors at 6.5 years using the Strengths and Difficulties Questionnaire (SDQ, range 0-40). Mixed-effects linear regression analyses corrected for clustering, adjusted for the randomized intervention group and baseline parental sociodemographic characteristics, and were considered mediation by child BMI., Results: Among 11 276 participants, 9355 women (83%) were aged 20 to 34 years, 10 128 (89.8%) were married, and 11 050 (98.0%) did not smoke during pregnancy. Each 5-unit increase in of maternal late-pregnancy BMI (mean [SD], 27.2 [3.8]) was associated with lower offspring WASI performance intelligence quotient (IQ) (-0.52 points; 95% CI, -0.87 to -0.17 points) at 6.5 years and lower scores on 5 of 7 NeuroTrax subscales and the global cognitive score at 16 years (-0.67 points; 95% CI, -1.06 to -0.29 points). Results were similar after adjustment for sociodemographic characteristics, pregnancy complications, and paternal BMI and were not mediated by child weight. Higher late pregnancy maternal BMI was also associated with more behavioral problems reported on the SDQ by teachers but not associated with parent-reported behaviors (externalizing behaviors: 0.13 points; 95% CI, 0.02 to 0.24 points; and total difficulties: 0.14 points, 95% CI, -0.02 to 0.30 points). Results were similar for maternal BMI measured in the first trimester or postpartum. In contrast, higher 6.5-year paternal BMI was associated with slightly better child cognition (WASI verbal IQ: 0.42 points; 95% CI, 0.02 to 0.82 points; NeuroTrax executive function score: 0.68 points; 95% CI, 0.24 to 1.12 points) and fewer teacher-reported behavioral problems (total difficulties: -0.29 points; 95% CI, -0.46 to -0.11 points)., Conclusions and Relevance: This cohort study supports findings from animal experiments and human observational studies in settings with higher maternal BMI and obesity rates. Higher maternal prenatal BMI may be associated with poorer offspring brain development, although residual confounding cannot be excluded.