Two requirements to utilise the large source of time-series sensor data from the Internet of Things are interoperability and efficient access. We present a Linked Data solution that increases interoperability through the use and referencing of common identifiers and ontologies for integration. From our study of the shape of Internet of Things data, we show how we can improve access within the resource constraints of Lightweight Computers, compact machines deployed in close proximity to sensors, by storing time-series data succinctly as rows and producing Linked Data ‘just-in-time’. We examine our approach within two scenarios: a distributed meteorological analytics system and a smart home hub. We show with established benchmarks that in comparison to storing the data in a traditional Linked Data store, our approach provides gains in both storage efficiency and query performance from over 3 times to over three orders of magnitude on Lightweight Computers. Finally, we reflect how pushing computing to edge networks with our infrastructure can affect privacy, data ownership and data locality.