Given a set of potential facility location sites along with a positive weight associated with each site as per its importance, the anti-covering location problem (ACLP) is about locating a set of facilities at some of these potential locations such that no two facilities are closer than a given distance from each other and sum of weights of chosen locations is as large as possible. This NP-hard problem has several important real-world applications such as telecommunications equipment siting, locating military units, locating franchise outlets, locating obnoxious facilities, forest management and DNA sequence matching. There are weighted and unweighted versions of ACLP. The unweighted version of ACLP is widely studied in the literature. However, the weighted version did not receive much attention despite several real-world applications. In this paper, we have proposed two evolutionary approaches based on genetic algorithm (GA) and discrete differential evolution (DDE) to solve the weighted version of the ACLP. The proposed approaches are used to solve the 80 ACLP instances with upto 1577 potential sites. Computational results show the effectiveness of our approaches.