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 are many studies on LBW, but only a small proportion has examined local geographical patterns in LBW and its determinants. LBW is a particular health concern in Mexico. The study aims to: (i) model the change in the LBW risk at the municipality level in Greater Mexico City, identifying municipalities with highest and lowest LBW risk; and (ii) explore the role of some socioeconomic and demographic risk factors in explaining LBW variations. We propose a Bayesian spatio-temporal analysis to control for space-time patterning of the data and for maternal age and prenatal care, both found to be important LBW determinants. Most of the high-risk municipalities are in the south-west and west of Greater Mexico City; and although for many of these municipalities the trend is stable, some present an increasing LBW risk over time. The results also identify those with medium-risk and with an increasing trend. These findings can support decision-makers in geographical targeting efforts to address spatial health inequalities, they may also facilitate a more proactive and cost-efficient approach to reduce LBW risk.