There is strong evidence that low birth weight (LBW) has a negative impact on infants' health. Children with LBW are more vulnerable to having disabilities. There has been a considerable amount of research on LBW, but only a small proportion of this research has examined local geographical patterns in LBW and its determinants. LBW is a particular health concern in Mexico. The aims of this study are to: (i) model the change in the LBW risk at the municipality level for the Greater Mexico City area, identifying municipalities with highest and lowest LBW risks; and (ii) explore the role of some socioeconomic and demographic risk factors in explaining variations in LBW. We propose a Bayesian spatio-temporal analysis to control for space-time patterning of the data. The analysis controls for maternal age and prenatal care, both found to be important determinants of LBW. Most of the high-risk municipalities are in the south-west and west of the Greater Mexico City area; and even though for the majority of these municipalities the trend is stable, some present an increasing LBW risk over time. The results also identify those with medium-risk, but also with increasing trend. These findings can support policy makers and other stakeholders in geographical targeting efforts to address the spatial health inequalities, and as a tool to facilitate a more proactive, cost-efficient approach to reduce LBW risk.