This paper combines a theoretical and an empirical approach to address how health at birth affects child development? Using a simple theoretical model in which parents invest in their children, we identify the mechanisms through which better health at birth can improve child development. We also emphasise how parental socioeconomic status can shape the effects of health at birth. We perform an empirical analysis on a French cohort of children born in 2011, using a unique dataset ELFE. We identify the effect of birth weight and gestational age on child development at one year. The results indicate that only gestational age positively affects early development. We find no empirical evidence for the existence of a severity effect, according to which the adverse effects of poor health at birth are higher for children in low-income families or with poorly educated mothers.