As a distributed ledger, blockchain inherently guarantees data consistency. However, when applied to the Internet of Things (IoT), existing solutions employing blockchain systems struggle to address the scalability demands posed by the dynamic mobility of heterogeneous devices. To this end, we propose Lightweight DAG Chain (LDChain), a lightweight and scalable blockchain system tailored for IoT scenarios. LDChain connects weak nodes and strong nodes through a hierarchical DAG consensus algorithm. For weak nodes, we introduce a transaction-based DAG consensus mechanism utilizing a snapshot synchronization strategy to cater to the dynamic nature of weak nodes and the scalability demands of the system. The integrated snapshot synchronization strategy, based on the second latest block transaction selection algorithm, reduces the storage and computational overhead for resource-restricted devices. For strong nodes, we devise a block-based DAG consensus mechanism and a repackaging strategy, which resolves transaction conflicts across regions by managing conflicting transactions through a priority queue. We implement a prototype of LDChain and conduct experiments in a network environment comprising 10 cloud servers, simulating several strong nodes and weak nodes. The experimental results show that our system achieves a throughput exceeding 7000 transactions per second (TPS) and a transaction confirmation latency of 1.3 s with 100 nodes.