Research has previously shown a gap of near 0.5 of a standard deviation (SD) in cognition and language development between the top and bottom household wealth quartile in children aged 6–42 months in a large representative sample of low- and middle-income families in Bogota, using the Bayley Scales of Infant and Toddler Development. The gaps in fine motor and socio-emotional development were about half that size. Developmental deficits increased with age. The current study explored the associations amongst child development, household socio-economic status (SES), and a set of potential mediating variables—parental characteristics, child biomedical factors, and the quality of the home environment—in this sample. We ran mediation tests to quantify the contribution of these variables to the SES gap, and explored the role of age as a moderator. Parental education, particularly maternal education, and the quality of the home environment mediated the SES gap in all outcomes examined. Height-for-age mediated a small amount of the deficit in language scales only. More educated mothers provided better home stimulation than less educated mothers and the home environment partly mediated the effect of maternal education. These results suggested that in interventions aimed at promoting child development, those focusing on the quality of the home environment should be effective.