Several studies have demonstrated the benefits of using a mobile sink to reduce the energy consumption of nodes and to prevent the formation of energy holes in wireless sensor networks (WSNs). However, these benefits are dependent on the path taken by the mobile sink, particularly in delay-sensitive applications, as all sensed data must be collected within a given time constraint. An approach proposed to address this challenge is to form a hybrid moving pattern in which a mobile-sink node only visits rendezvous points (RPs), as opposed to all nodes. Sensor nodes that are not RPs forward their sensed data via multihopping to the nearest RP. The fundamental problem then becomes computing a tour that visits all these RPs within a given delay bound. Identifying the optimal tour, however, is an NP-hard problem. To address this problem, a heuristic called weighted rendezvous planning (WRP) is proposed, whereby each sensor node is assigned a weight corresponding to its hop distance from the tour and the number of data packets that it forwards to the closest RP. WRP is validated via extensive computer simulation, and our results demonstrate that WRP enables a mobile sink to retrieve all sensed data within a given deadline while conserving the energy expenditure of sensor nodes. More specifically, WRP reduces energy consumption by 22% and increases network lifetime by 44%, as compared with existing algorithms.