Socioeconomically disadvantaged children are more likely to be of shorter stature and overweight, leading to greater risk of obesity in adulthood. Disentangling the mediatory pathways between socioeconomic disadvantage and childhood size may help in the development of appropriate policies aimed at reducing these health inequalities. We aimed to elucidate the putative mediatory role of birth weight using a representative sample of the Scottish population born 1991–2001 (n = 16,628). Estimated height and overweight/obesity at age 4.5 years were related to three measures of socioeconomic disadvantage (mother’s education, Scottish Index of Multiple Deprivation, synthetic weekly income). Mediation was examined using two approaches: a ‘traditional’ mediation analysis and a counterfactual-based mediation analysis. Both analyses identified a negative effect of each measure of socioeconomic disadvantage on height, mediated to some extent by birth weight, and a positive ‘direct effect’ of mother’s education and Scottish Index of Multiple Deprivation on overweight/obesity, which was partly counterbalanced by a negative ‘indirect effect’. The extent of mediation estimated when adopting the traditional approach was greater than when adopting the counterfactual-based approach because of inappropriate handling of intermediate confounding in the former. Our findings suggest that higher birth weight in more disadvantaged groups is associated with reduced social inequalities in height but also with increased inequalities in overweight/obesity.