We propose WEAVE, a geographical 2D/3D routing protocol that maintains information on a small number of waypoints and checkpoints for forwarding packets to any destination. Nodes obtain the routing information from partial traces gathered in incoming packets and use a system of checkpoints along with the segments of routes to weave end-to-end paths close to the shortest ones. WEAVE does not generate any control traffic, it is suitable for routing in both 2D and 3D networks, and does not require any strong assumption on the underlying network graph such as the Unit Disk or a Planar Graph. WEAVE compares favorably with existing protocols in both testbed experiments and simulations.