Young adulthood is a crucial period for major physiological transitions. Environmental changes associated with these transitions can influence health behaviour and health (e.g. poor diet, high body weight and elevated blood pressure (EBP)). Excess body weight can lead to EBP; however, little is known about this relationship among young adults in developing countries. Focusing on Bangladesh, this study assessed the association between BMI and blood pressure (BP) metrics (systolic BP (SBP), diastolic BP (DBP) and BP class (optimal, normal/high normal and elevated)). Sex-specific analyses of these relationships were performed to assess any difference across sexes. Furthermore, associations of overweight/obesity with BP metrics were investigated. Young adults aged 18–24 years (n 2181) were included from nationally representative cross-sectional Bangladesh Demographic and Health Survey 2017–2018. Multivariable linear and multinomial logistic regression models examined the relationships between BMI, overweight/obesity and BP metrics. Findings reveal that higher BMI was associated with higher SBP (0·83; 95 % CI 0·67, 0·99), DBP (0·66; 95 % CI 0·54, 0·74) and higher odds of having EBP (adjusted OR 1·24; 95 % CI 1·17, 1·31). These relationships were stronger among males than females. Moreover, overweight/obese individuals had higher SBP, DBP and higher odds of having EBP than individuals with normal BMI. Strategies to reduce body weight and to improve healthy lifestyle, and awareness and monitoring of BP may help to address these serious health problems, particularly at an early age.