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We consider the problem of assigning tasks and related trajectories to a fleet of drones, in critical scenarios requiring early anomaly discovery and intervention. Drones visit target points in consecutive trips, with recharging and data offloading in between. We propose a novel metric, called weighted coverage, which generalizes classic notions of coverage, as well as a new notion of accumulative coverage which prioritizes early inspection of target points. We formulate an ILP problem for weighted coverage maximization and show its NP-hardness. We propose an efficient polynomial algorithm with guaranteed approximation. By means of simulations we show that our algorithm performs close to the optimal solution and outperforms a previous approach in terms of several performance metrics, including coverage, average inspection delay, energy consumption, and computation time, under a wide range of application scenarios.