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Despite a decrease in the prevalence of low birth weight (LBW) over time, its ongoing significance as a public health concern in Bangladesh remains evident. Low birth weight is believed to be a contributing factor to infant mortality, prolonged health complications, and vulnerability to non-communicable diseases. This study utilizes nationally representative data from the Multiple Indicator Cluster Surveys (MICS) conducted in 2012-2013 and 2019 to explore factors associated with birth weight. Modeling birth weight data considers interactions among factors, clustering in data, and spatial correlation. District-level maps are generated to identify high-risk areas for LBW. The average birth weight has shown a modest increase, rising from 2.93 kg in 2012-2013 to 2.96 kg in 2019. The study employs a regression tree, a popular machine learning algorithm, to discern essential interactions among potential determinants of birth weight. Findings from various models, including fixed effect, mixed effect, and spatial dependence models, highlight the significance of factors such as maternal age, household head's education, antenatal care, and few data-driven interactions influencing birth weight. District-specific maps reveal lower average birth weights in the southwestern region and selected northern districts, persisting across the two survey periods. Accounting for hierarchical structure and spatial autocorrelation improves model performance, particularly when fitting the most recent round of survey data. The study aims to inform policy formulation and targeted interventions at the district level by utilizing a machine learning technique and regression models to identify vulnerable groups of children requiring heightened attention.