We describe a novel constraint-based approach to approximate ISP link weights using only end-to-end measurements. Common routing protocols such as OSPF and IS-IS choose least-cost paths using link weights, so inferred weights provide a simple, concise, and useful model of intradomain routing. Our approach extends router-level ISP maps, which include only connectivity, with link weights that are consistent with routing. Our inferred weights agree well with observed routing: while our inferred weights fully characterize the set of shortest paths between 84-99% of the router-pairs, alternative models based on hop count and latency do so for only 47-81% of the pairs.