Multiplying the heuristic function by a weight greater than one is a well-known technique in Heuristic Search. When applied to A* with an admissible heuristic it yields substantial runtime savings, at the expense of sacrificing solution optimality. Only a few works have studied the applicability of this technique to Real-Time Heuristic Search (RTHS), a search approach that builds upon Heuristic Search. In this paper we present two novel approaches to using weights in RTHS. The first one is a variant of a previous approach by Shimbo and Ishida. It incorporates weights to the lookahead search phase of the RTHS algorithm. The second one incorporates the weight to the edges of the search graph during the learning phase. Both techniques are applicable to a wide class of RTHS algorithms. Here we implement them within LSS-LRTA * and LRTA*-LS, obtaining a family of new algorithms. We evaluate them in path-planning benchmarks and show the second technique yields improvements of up to one order-of-magnitude both in solution cost and total search time. The first technique, on the other hand, yields poor results. Furthermore, we prove that RTHS algorithms that can appropriately use our second technique terminate finding a solution if one exists. Copyright © 2013, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.