Asynchronous federated learning (AFL) is essential for low-altitude networks due to its benefits in reducing communication bandwidth, lowering transmission delays, and preserving data privacy. However, the highly dynamic mobility of drones, combined with inherent heterogeneities in AFL, including variations in data volume, data distribution, and device capability, introduces severe challenges, such as inconsistent model update frequencies, biased local training, and inefficient global aggregation. Consequently, these issues lead to significant accuracy degradation and hinder practical deployment. In this paper, we propose a novel AFL framework tailored for low-altitude networks to address these challenges, which combines a multi-dimensional clustering mechanism with a multi-weight aggregation mechanism (MDC-MWA). To mitigate local model bias induced by data heterogeneity, the multi-dimensional clustering allows the cloud server to compute a comprehensive score for each drone based on multiple dimensions, including the label distribution, the gradient direction, and the local data proportion. It then employs K-Means clustering to partition drones into highly homogeneous subgroups, each managed by a dedicated roadside unit (RSU). Within each subgroup, after performing local updates, each drone synchronously uploads parameters to its RSU. Between these subgroups, to address inconsistent update frequencies caused by imbalanced computing capabilities, RSUs perform asynchronous training via the multi-weight aggregation mechanism, which updates the global model considering staleness weight and direction consistency weight. Experimental results demonstrate that the proposed method outperforms baseline approaches in highly heterogeneous scenarios, achieving a 4.74% absolute improvement in training accuracy on the CIFAR-10 dataset. This work provides a practical framework for distributed intelligent applications in dynamic and resource-constrained low-altitude networks.