The impressive success of Generative Adversarial Networks (GANs) is often overshadowed by the difficulties in their training. Despite the continuous efforts and improvements, there are still open issues regarding their convergence properties. In this paper, we propose a simple training variation where suitable weights are defined and assist the training of the Generator. We provide theoretical arguments which indicate that the proposed algorithm is better than the baseline algorithm in the sense of creating a stronger Generator at each iteration. Performance results showed that the new algorithm is more accurate and converges faster in both synthetic and image datasets resulting in improvements ranging between 5% and 50%.