A novel Weighted Bipolar Argumentation Framework (WBAF) is proposed in this paper, which deals with attack and support relations equally and takes into account the weight of arguments and relations, and is a more general extension of the classical AF. The semantics of WBAF - minimum-penalty preferred extensions is introduced, which refers to the maximal acceptable argument set inclusions. Furthermore, this paper designs and realizes an ASP-based WBAF reasoning tool - ASPWBART (Answer Set Programming Based Weighted Bipolar Argumentation Reasoning Tool). This tool supports the incorporation of weighted arguments and weighted relations, and culminates in the generation of minimum-penalty preferred extensions.