Unmanned aerial vehicles (UAVs) are increasingly being deployed in logistics, service robotics, and other real-world applications, creating a growing demand for autonomous payload acquisition and delivery. Existing approaches typically assume pre-attached payloads or rely on specialized grippers, leaving versatile end-to-end aerial delivery largely unresolved, where different payloads induce highly variable flight dynamics, requiring a single policy to adapt online without manual calibration or explicit system identification. To this end, we study \textbf{A}utonomous \textbf{A}erial Manipulation via \textbf{Co}ntextual \textbf{Co}ntrastive Meta Reinforcement Learning (\textbf{\textit{Aco2}}), a fully autonomous aerial delivery setting in which a quadrotor equipped with a lightweight hook continuously picks up, transports, and delivers diverse handle-equipped objects between randomized locations, all without human intervention. First, we design a contextual observation encoder that infers a compact latent context from recent interaction history, enabling the policy to adapt online to payload-dependent dynamics. To further improve the quality of this context, we introduce a contrastive objective that structures the context embedding around task-relevant variations, improving generalization across diverse payloads without requiring explicit system identification. Trained entirely in simulation with extensive domain randomization, \textit{Aco2} can be directly deployed on a physical quadrotor without real-world fine-tuning.