Weak coin flipping is a cryptographic primitive in which two mutually distrustful parties generate a shared random bit to agree on a winner via remote communication. While a stand-alone secure weak coin flipping protocol can be constructed from noiseless quantum communication channels, its composability remains unexplored. In this work, we demonstrate that no weak coin flipping protocol can be abstracted as a simple black-box resource with composable security. Despite this, we also establish the overall stand-alone security of quantum weak coin flipping protocols under composition in sequential order.