The co-existence of under- and overweight at population level around the globe is well documented. However, this has yet to be explored using suitable statistical techniques in the context of Bangladesh. This study aimed to examine the prevalence and risk factors for being underweight and overweight or obese compared with normal weight in ever-married non-pregnant women aged 15-49 years in Bangladesh using data from the most recent Bangladesh Demographic and Health Survey conducted in 2014. Multilevel multinomial logistic regression (MLMLR) and quantile regression models were fitted to examine the associations of socioeconomic and individual-, household- and community-level factors on the nutritional status of women as measured by BMI. Overall, the prevalences of underweight, normal weight, overweight and obese women were 19%, 58%, 19% and 4%, respectively, in 2014. The MLMLR analysis revealed that women of young age, widowed/divorced/separated, having a larger family size and children aged ≤5 years in the household, currently amenorrhoeic and members of non-government organizations were at significantly increased risk of being underweight; those of older age, having higher parity, more educated, frequently watched TV and non-poor were more likely to be overweight or obese relative to normal BMI. Women from more affluent communities and urban areas were more likely to be overweight or obese relative to normal BMI than their counterparts from less-affluent and rural communities. Women's nutritional status was found to be heterogeneous across the regions of the country. The findings indicate that, along with individual-level factors, community-level characteristics are also important in explaining women's BMI in Bangladesh. The issue of under- and overweight or obesity among women in Bangladesh requires the immediate adoption of a public health policy for its mitigation. When developing intervention programmes, important determinants and uniform development of regions should be taken into consideration to combat the dual burden of under- and overweight among women in Bangladesh.