We propose a new switching criterion, namely the evenness or unevenness of the distribution of variable weights, and use this criterion to combine intensification and diversification in local search for SAT. We refer to the ways in which state-of-the-art local search algorithms adaptG2WSATP and VW select a variable to flip, as heuristic adaptG2WSATP and heuristic VW, respectively. To evaluate the effectiveness of this criterion, we apply it to heuristic adaptG2WSATP and heuristic VW, in which the former intensifies the search better than the latter, and the latter diversifies the search better than the former. The resulting local search algorithm, which switches between heuristic adaptG2WSATP and heuristic VW in every step according to this criterion, is called Hybrid. Our experimental results show that, on a broad range of SAT instances presented in this paper, Hybrid inherits the strengths of adaptG2WSATP and VW, and exhibits generally better performance than adaptG2WSATP and VW. In addition, Hybrid compares favorably with state-of-the-art local search algorithm R+adaptNovelty+ on these instances. Furthermore, without any manual tuning parameters, Hybrid solves each of these instances in a reasonable time, while adaptG2WSATP, VW, and R+adaptNovelty+ have difficulty on some of these instances.