Conventional functional connectivity network (FCN) based on resting-state fMRI (rs-fMRI) can only reflect the relationship between pairwise brain regions. Thus, the hyper-connectivity network (HCN) has been widely used to reveal high-order interactions among multiple brain regions. However, existing HCN models are essentially spatial HCN, which reflect the spatial relevance of multiple brain regions, but ignore the temporal correlation among multiple time points. Furthermore, the majority of HCN construction and learning frameworks are limited to using a single template, while the multi-template carries richer information. To address these issues, we first employ multiple templates to parcellate the rs-fMRI into different brain regions. Then, based on the multi-template data, we propose a spatio-temporal weighted HCN (STW-HCN) to capture more comprehensive high-order temporal and spatial properties of brain activity. Next, a novel deep fusion model of multi-template called spatio-temporal weighted multi-hypergraph convolutional network (STW-MHGCN) is proposed to fuse the STW-HCN of multiple templates, which extracts the deep interrelation information between different templates. Finally, we evaluate our method on the ADNI-2 and ABIDE-I datasets for mild cognitive impairment (MCI) and autism spectrum disorder (ASD) analysis. Experimental results demonstrate that the proposed method is superior to the state-of-the-art approaches in MCI and ASD classification, and the abnormal spatio-temporal hyper-edges discovered by our method have significant significance for the brain abnormalities analysis of MCI and ASD.