Federated learning offers a promising approach under the constraints of networking and data privacy constraints in aerial and space networks (ASNs), utilizing large-scale private edge data from drones, balloons, and satellites. Existing research has extensively studied the optimization of the learning process, computing efficiency, and communication overhead. An important yet often overlooked aspect is that participants contribute predictive knowledge with varying diversity of knowledge, affecting the quality of the learned federated models. In this paper, we propose a novel approach to address this issue by introducing a Weighted Averaging and Client Selection (WeiAvgCS) framework that emphasizes updates from high-diversity clients and diminishes the influence of those from low-diversity clients. Direct sharing of the data distribution may be prohibitive due to the additional private information that is sent from the clients. As such, we introduce an estimation for the diversity using a projection-based method. Extensive experiments have been performed to show WeiAvgCS's effectiveness. WeiAvgCS could converge 46% faster on FashionMNIST and 38% faster on CIFAR10 than its benchmarks on average in our experiments.