The booming development of the fifth generation mobile communication technology and even 6G has given rise to further demanding requirements for communication transmission quality, capacity, and rate. This paper considers the issues related to the weighted sum rate using intelligent reflecting surface assisted rate-splitting multiple access for downlink multiuser MISO systems. The aim to devise a scheme to obtain the maximum weighted sum rate by optimizing the equivalent beam forming matrix, quantized IRS phase shift matrix, and the common rate splitting scheme. To this end, an equivalent optimization scheme is designed based on the weighted MMSE algorithm, intersection representation of convex sets and Taylor approximation, where the non-convex combinatorial optimization problem is converted to a convex optimization problem and solved iteratively using the alternating optimization algorithm. The paper compares the maximum weighted sum rate achievable by quantized IRS-aided 1-layer-RSMA and three other multiple access technologies: DPC, NOMA, and MULP under different SNR scenarios. It is also found that the proposed method brings about an improvement in weighted sum rate with the increase in the number of antennas, the number of IRS reflective elements and the number of phase quantization bits. The research results provide a reference for the engineering design of communication systems.