Traditional Internet of Things (IoT) architectures that rely on centralized servers for data management and decision-making are vulnerable to security threats and privacy leakage. To address this issue, blockchain has been advocated for decentralized data management in a tamper-resistance, traceable, and transparent manner. However, a major issue that hinders the integration of blockchain and IoT lies in that, it is rather challenging for resource-constrained IoT devices to perform computation-intensive blockchain consensuses such as Proof-of-Work (PoW). Furthermore, the incentive mechanism of PoW pushes lightweight IoT nodes to aggregate their computing power to increase the possibility of successful block generation. Nevertheless, this eventually leads to the formation of computing power alliances, and significantly compromises the decentralization and security of BlockChain-aided IoT (BC-IoT) networks. To cope with these issues, we propose a lightweight consensus protocol for BC-IoT, called Proof-of-Trusted-Work (PoTW). The goal of the proposed consensus is to disincentivize the centralization of computing power and encourage the independent participation of lightweight IoT nodes in blockchain consensus. First, we put forth an on-chain reputation evaluation rule and a reputation chain for PoTW to enable the verifiability and traceability of nodes' reputations based on their contributions of computing power to the blockchain consensus, and we incorporate the multi-level block generation difficulty as a rewards for nodes to accumulate reputations. Second, we model the block generation process of PoTW and analyze the block throughput using the continuous time Markov chain. Additionally, we define and optimize the relative throughput gain to quantify and maximize the capability of PoTW that suppresses the computing power centralization (i.e., centralization suppression). Furthermore, we investigate the impact of the computing power of the computing power alliance and the levels of block generation difficulty on the centralization suppression capability of PoTW. Finally, simulation results demonstrate the consistency of the analytical results in terms of block throughput. In particular, the results show that PoTW effectively reduces the block generation proportion of the computing power alliance compared with PoW, while simultaneously improving that of individual lightweight nodes. This indicates that PoTW is capable of suppressing the centralization of computing power to a certain degree. Moreover, as the levels of block generation difficulty in PoTW increase, its centralization suppression capability strengthens.