It is critical to design efficient beamforming in reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) systems for enhancing spectrum utilization. However, conventional methods often have limitations, either incurring high computational complexity due to iterative algorithms or sacrificing performance when using heuristic methods. To simultaneously achieve both low complexity and high spectrum efficiency, lightweight structures are employed to develop an unsupervised learning-based beamforming design in this letter. We tailor image-shaped channel samples and develop an ISAC beamforming neural network (IBF-Net) model. By leveraging unsupervised learning, the loss function incorporates key performance metrics like sensing and communication channel correlation and sensing channel gain, eliminating the need for labeling. Simulations show that the proposed method achieves competitive performance compared to the benchmarks and significantly reduces the computational complexity.