The association between birth weight and mortality is among the strongest seen in epidemiology. While preterm delivery causes both small babies and high mortality, it does not explain this association. Fetal growth restriction has also been proposed, although its features are unclear because it lacks a definition independent of weight. If, as some postulate, birth weight is not itself on the causal path to mortality, its relation with mortality would have to be explained by confounding factors that decrease birth weight and increase mortality. In this paper, the authors explore the characteristics such confounders would require in order to achieve the observed association between birth weight and mortality. Through a simple simulation, they found that the observed steep gradient of risk for small babies at term can be produced by a rare condition or conditions (with a total prevalence of 0.5%) having profound effects on both fetal growth (-1.7 standard deviations) and mortality (relative risk = 160). Candidate conditions might include malformations, fetal or placental aneuploidy, infections, or imprinting disorders. If such rare factors underlie the association of birth weight with mortality, it would have broad implications for the study of fetal growth restriction and birth weight, and for the prevention of infant mortality.