As the Internet of Things and mobile Internet technologies continue to advance, a wide range of mobile devices are connected to the Internet. To identify and authenticate these devices, it is necessary to verify the digital signatures they submit. However, many mobile devices have limited computing power and typically use software modules to store keys locally or on smart chips, which increases the risk of key exposure. To avoid this risk, threshold signatures are commonly employed in real-world applications. These signatures rely on multi-party cooperation to decentralize risks and enhance device availability. The SM2 digital signature algorithm, an elliptic curve public key cryptographic algorithm developed independently by China, was adopted as the national cryptography standard in 2016. It finds extensive use in various sectors including government agencies, financial institutions, and electronic authentication service providers. While there has been interest in constructing SM2 threshold signatures with high availability, there are still limited schemes available, and participant weights have not been adequately considered. This study proposes a flexible SM2 weighted threshold signature scheme. In this scheme, signers are assigned different weights, and multiple signers collaborate to generate a valid signature. The key of the SM2 digital signature is divided based on the weighted threshold secret sharing of the Chinese remainder theorem. Participants do not acquire a signing key only by meeting the threshold value. They have to meet the corresponding secret threshold t and the reconstruction threshold T by calculating the sum of the weights of participants to obtain part of the key information or recover the signing key. During secret segmentation, the private signing key of the SM2 digital signature algorithm is transformed to complete the inversion of the SM2 key during the signing stage. Finally, the proposed scheme is compared with other schemes such as SM2 threshold signatures and joint SM2 signatures. The proposed scheme not only reduces computational overhead but also enhances the functionality of the SM2 signature.