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Distributed Ledger Technologies (DLTs) are playing a major role in building security and trust in Internet of Things (IoT) systems. However, IoT deployments with a large number of devices, such as in environment monitoring applications, generate and send massive amounts of data. This would generate vast number of transactions that must be processed within the distributed ledger. In this work, we first demonstrate that the Proof of Work (PoW) blockchain fails to scale in a sizable IoT connectivity infrastructure. To solve this problem, we present a lightweight distributed ledger scheme to integrate PoW blockchain into IoT. In our scheme, we classify transactions into two types: 1) global transactions, which must be processed by global blockchain nodes and 2) local transactions, which can be processed locally by entities called witnesses. Performance evaluation demonstrates that our proposed scheme improves the scalability of integrated blockchain and IoT monitoring systems by processing a fraction of the transactions, inversely proportional to the number of witnesses, locally. Hence, reducing the number of global transactions.