Given a data graph G, a source vertex u and a target vertex v of a reachability query, the reachability query is used to answer whether there exists a path from u to v in G. Reachability query processing is one of the fundamental operations in graph data management, which is widely used in biological networks, communication networks, and social networks to assist data analysis. The data graphs in practical applications usually contain information such as quantization weights associated with the structural relationships, in addition to the structural relationships between vertices. Thus, in addition to the traditional reachability relationships, users may want to further understand whether such reachability relationships satisfy specific constraints. In this paper, we study the problem of efficiently processing k -step reachability queries with weighted constraints in weighted graphs. The k -step weighted reachability query questions are used to answer the question of whether there exists a path from a source vertex u to a goal vertex v in a given weighted graph. If it exists, the path needs to satisfy 1) all edges in the path satisfy the given weight constraints, and 2) the length of the path does not exceed the given distance threshold k. To address the problem, firstly, WKRI index supporting k -step weighted reachability query processing and index construction methods based on efficient pruning strategies are proposed. Secondly, the idea of constructing index based on part of the vertexs is proposed to reduce the size of the index. We design and implement two optimized indexes GWKRI and LWKRI based on the vertex coverage set. Finally, experiments are conducted on several real datasets. The experimental results verify the efficiency of the method proposed in this paper in answering k -step weighted reachability queries.