A well-functioning placenta is essential for fetal and maternal health throughout pregnancy. Using placental weight as a proxy for placental growth, we report genome-wide association analyses in the fetal (n = 65,405), maternal (n = 61,228) and paternal (n = 52,392) genomes, yielding 40 independent association signals. Twenty-six signals are classified as fetal, four maternal and three fetal and maternal. A maternal parent-of-origin effect is seen near KCNQ1. Genetic correlation and colocalization analyses reveal overlap with birth weight genetics, but 12 loci are classified as predominantly or only affecting placental weight, with connections to placental development and morphology, and transport of antibodies and amino acids. Mendelian randomization analyses indicate that fetal genetically mediated higher placental weight is causally associated with preeclampsia risk and shorter gestational duration. Moreover, these analyses support the role of fetal insulin in regulating placental weight, providing a key link between fetal and placental growth.