The emergence of edge computing has witnessed a fast-growing volume of data on edge devices belonging to different stakeholders which, however, cannot be shared among them due to the lack of the trust. By exploiting blockchain's non-repudiation and non-tampering properties that enable trust, we develop a blockchain-based big data sharing framework to support various applications across resource-limited edges. In particular, we devise a number of novel resource-efficient techniques for the framework: (1) the PoC (Proof-of-Collaboration) based consensus mechanism with low computation complexity which is especially beneficial to the edge devices with low computation capacity, (2) the blockchain transaction filtering and offloading scheme that can significantly reduce the storage overhead, and (3) new types of blockchain transaction (i.e., Express Transaction) and block (i.e., Hollow Block) to enhance the communication efficiency. Extensive experiments are conducted and the results demonstrate the superior performance of our proposal.