A large literature has established a causal link between child birth weight and long life human capital. In this paper we ask to what extent household resources are able to insure the child against this early life health shock. We address the double endogeneity of birth weight and resources by using, on the one hand, twin difference estimation and, on the other hand, variation in economic resources between twins born in regions exposed and not exposed to the 70s Norwegian oil shock, a natural resource boom that resulted in a semi-permanent income shock. For children born full-term, we find that exposure to the oil shock attenuates the negative effect of low birth weight on a range of human capital outcomes, including schooling and earnings. We provide evidence that the father’s labour income is a potential mechanism through which the oil shock protects children against low birth weight, while there is no role coming from local public expenditure. However, for pre-term births, we find that it is not always possible to remedy for low birth weight by increasing economic resources.