In recent years, the increasing demand for parameter-efficient automatic speech recognition (ASR) systems has driven researchers to explore innovative architectures and techniques designed for minimising model size while maintaining recognition performance. Thus, weight-sharing mechanisms stand out as a promising approach. In this study, we present a comprehensive evaluation of weight-sharing applied to the different components of both Transformer and Conformer architectures in the context of ASR. Furthermore, we investigate the behaviour of these weight-sharing configurations when fine-tuned for a low-resource task, specifically children's ASR. Additionally, we introduce Shared-Conformer, a novel architecture that achieves a 63% parameter reduction with only a minimal increase in word error rate. Our findings demonstrate that weight-sharing significantly reduces the number of parameters while preserving competitive performance in both well-resourced and low-resourced scenarios.