Video-based sensing from aerial drones, especially small multirotor drones, can provide rich data for numerous applications, including traffic analysis (computing traffic flow volumes), precision agriculture (periodically evaluating plant health), and wildlife population management (estimating population sizes). However, aerial drone video sensing applications must handle a surprisingly wide range of tasks: video frames must be aligned so that we can equate coordinates of objects that appear in different frames, video data must be analyzed to extract application-specific insights, and drone routes must be computed that maximize the value of newly captured video. To address these challenges, we built SkyQuery, a novel aerial drone video sensing platform that provides an expressive, high-level programming language to make it straightforward for users to develop complex long-running sensing applications. SkyQuery combines novel methods for fast video frame alignment and detection of small objects in top-down aerial drone video to efficiently execute applications with diverse video analysis workflows and data distributions, thereby allowing application developers to focus on the unique qualities of their particular application rather than general video processing, data analysis, and drone routing tasks. We conduct diverse case studies using SkyQuery in parking monitoring, pedestrian activity mapping, and traffic hazard detection scenarios to demonstrate the generalizability and effectiveness of our system.