Light sailing is the only existing in-space propulsion technology that could allow us to visit other star systems in a human lifespan. In order to best harness radiation pressure, light sails need to be highly reflective, lightweight and mechanically robust. This is traditionally achieved by the use of nanometer-thin reflective layers supported by a micrometer-thick substrate that endows them with the necessary sturdiness. This combination usually results in a sail mass that is too high to be efficiently used for extrasolar exploration. Here, we propose a potentially scalable sail design that combines a hollow substrate with an atomically-thin 2D material which, thanks to its ultimately low surface density, allows reducing the mass contribution of the substrate. To demonstrate the potential of such sails, we have studied the laser-induced displacement of graphene-on-copper sails in vacuum and in microgravity. In these conditions, 0.25 mg samples are accelerated by using lasers of different wavelengths (450 and 655 nm) and power (0.1–1 W). The measured thrust is one order of magnitude larger than the theoretical calculations for radiation pressure alone. This calls for further theoretical studies and attracts interest on graphene as light-sail material.