Movable-antennas (MAs) are revolutionizing spatial signal processing by providing flexible beamforming in next-generation wireless systems. This paper investigates an MA-empowered autonomous aerial vehicle (AAV) system in low-altitude wireless networks (LAWNs) for uplink data collection from ground users. We aim to maximize the sum achievable rate by jointly optimizing the AAV trajectory, receive beamforming, and MA positions. An efficient alternating optimization (AO) algorithm that incorporates successive convex approximation, weighted minimum mean square error, and particle swarm optimization is developed. The analysis of the computational complexity and convergence features is provided. Extensive simulations demonstrate superior performance in terms of the sum achievable rate and the service reliability comparing to several benchmark schemes. These results demonstrate the distinctive advantages of the proposed scheme: enhanced spectral efficiency via adaptive beam-user alignment and improved collection reliability through spatial interference management, highlighting the implementation potential of the MA-empowered LAWNs.