Birth weight (BW) variation is influenced by fetal and maternal genetic and non-genetic factors, and has been reproducibly associated with future cardio-metabolic health outcomes. These associations have been proposed to reflect the lifelong consequences of an adverse intrauterine environment. In earlier work, we demonstrated that much of the negative correlation between BW and adult cardio-metabolic traits could instead be attributable to shared genetic effects. However, that work and other previous studies did not systematically distinguish the direct effects of an individual's own genotype on BW and subsequent disease risk from indirect effects of their mother's correlated genotype, mediated by the intrauterine environment. Here, we describe expanded genome-wide association analyses of own BW (n=321,223) and offspring BW (n=230,069 mothers), which identified 278 independent association signals influencing BW (214 novel). We used structural equation modelling to decompose the contributions of direct fetal and indirect maternal genetic influences on BW, implicating fetal- and maternal-specific mechanisms. We used Mendelian randomization to explore the causal relationships between factors influencing BW through fetal or maternal routes, for example, glycemic traits and blood pressure. Direct fetal genotype effects dominate the shared genetic contribution to the association between lower BW and higher type 2 diabetes risk, whereas the relationship between lower BW and higher later blood pressure (BP) is driven by a combination of indirect maternal and direct fetal genetic effects: indirect effects of maternal BP-raising genotypes act to reduce offspring BW, but only direct fetal genotype effects (once inherited) increase the offspring's later BP. Instrumental variable analysis using maternal BW-lowering genotypes to proxy for an adverse intrauterine environment provided no evidence that it causally raises offspring BP. In successfully separating fetal from maternal genetic effects, this work represents an important advance in genetic studies of perinatal outcomes, and shows that the association between lower BW and higher adult BP is attributable to genetic effects, and not to intrauterine programming.