Syntactic information is essential for both sentiment analysis(SA) and aspect-based sentiment analysis(ABSA). Previous work has already achieved great progress utilizing Graph Convolutional Network(GCN) over dependency tree of a sentence. However, these models do not fully exploit the syntactic information obtained from dependency parsing such as the diversified types of dependency relations. The message passing process of GCN should be distinguished based on these syntactic information. To tackle this problem, we design a novel weighted graph convolutional network(WGCN) which can exploit rich syntactic information based on the feature combination. Furthermore, we utilize BERT instead of Bi-LSTM to generate contextualized representations as inputs for GCN and present an alignment method to keep word-level dependencies consistent with wordpiece unit of BERT. With our proposal, we are able to improve the state-of-the-art on four ABSA tasks out of six and two SA tasks out of three.