Structured overlay networks that support range queries cannot hash data IDs for load balancing, in order to preserve the total order on the IDs. Since data and queries are not equally distributed on the ID-space without hashing in range-based overlay networks, uneven loads are imposed on the overlay nodes. Existing load balancing techniques for range-based overlay networks distribute the loads by using data reallocation or node migration, which makes the networks very unstable due to heavy data reallocation or frequent churn. This paper proposes a novel scheme that distributes, fairly, the loads without node migration and with little data reallocation, by sharing some ID-space regions between neighboring nodes. Our “overlapping” ID-space management scheme derives the optimal overlap based on kernel density estimations; the query loads based on the statistical theory are used to calculate the best overlap regions. This calculation is executed in a distributed manner with no central coordinator. We conduct thorough computer simulations, and show that our scheme alleviates the worst node load by 20–90 % against existing techniques without node migration and with least data reallocation.