Reconfigurable intelligent surface (RIS)-assisted cell-free (CF) multiple-input multiple-output (MIMO) networks can significantly enhance system performance. However, the extensive deployment of RIS elements imposes considerable channel acquisition overhead, with the high density of nodes and antennas in RIS-assisted CF networks amplifying this challenge. To tackle this issue, in this paper, we explore integrating RIS-user equipment (UE) association into downlink RIS-assisted CF transmitter design, which greatly reduces the channel acquisition costs. The key point is that once UEs are associated with specific RISs, there is no need to frequently acquire channels from non-associated RISs. Then, we formulate the problem of joint RIS-UE association and beamforming at APs and RISs to maximize the weighted sum rate (WSR). In particular, we propose a two-stage framework to solve it. In the first stage, we apply a many-to-many matching algorithm to establish the RIS-UE association. In the second stage, we introduce a sequential optimization-based method that decomposes the joint optimization of RIS phase shifts and AP beamforming into two distinct subproblems. To optimize the RIS phase shifts, we employ the majorization-minimization (MM) algorithm to obtain a semi-closed-form solution. For AP beamforming, we develop a joint block diagonalization algorithm, which yields a closed-form solution. Simulation results demonstrate the effectiveness of the proposed algorithm and show that, while RIS-UE association significantly reduces overhead, it incurs a minor performance loss that remains within an acceptable range. Additionally, we investigate the impact of RIS deployment and conclude that RISs exhibit enhanced performance when positioned between APs and UEs.