Intensification and diversification are the key factors that control the performance of stochastic local search in satisfiability (SAT). Recently, Novelty Walk has become a popular method for improving diversification of the search and so has been integrated in many well-known SAT solvers such as TNM and gNovelty+. In this paper, we introduce new heuristics to improve the effectiveness of NoveltyWalk in terms of reducing search stagnation. In particular, we use weights (based on statistical information collected during the search) to focus the diversification phase onto specific areas of interest. With a given probability, we select the most frequently unsatisfied clause instead of a totally random one as Novelty Walk does. Amongst all the variables appearing in the selected clause, we then select the least flipped variable for the next move. Our experimental results show that the new weight-enhanced diversification method significantly improves the performance of gNovelty + and thus outperforms other local search SAT solvers on a wide range of structured and random satisfiability benchmarks.