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The pervasive adoption of Internet-connected digital services has led to a growing concern in the personal data privacy of their customers. On the other hand, machine learning (ML) techniques have been widely adopted by digital service providers to improve operational productivity and customer satisfaction. ML inevitably accesses and processes users' personal data, which could potentially breach the relevant privacy protection regulations if not performed carefully. The situation is exacerbated by the cloud-based implementation of digital services when user data are captured and stored in distributed locations, hence aggregation of the user data for ML could be a serious breach of privacy regulations. In this backdrop, Federated Learning (FL) is an emerging area that allows ML on distributed data without the data leaving their stored location. However, depending on the nature of the digital services, data captured at different locations may carry different significance to the business operation, hence a weighted aggregation will be highly desirable for enhancing the quality of the FL-learned model. Furthermore, to prevent leakage of user data from the aggregated gradients, cryptographic mechanisms are needed to allow secure aggregation of FL. In this paper, we propose a privacy-enhanced FL scheme for supporting secure weighted aggregation. Besides, by devising a verification protocol based on Zero-Knowledge Proof (ZKP), the proposed scheme is capable of guarding against fraudulent messages from FL participants. Experimental results show that our scheme is practical and secure. Compared to existing FL approaches, our scheme achieves secure weighted aggregation with an additional security guarantee against fraudulent messages with an affordable 1.2 times runtime overheads and 1.3 times communication costs.