We demonstrate an autonomous, high-throughput mechanism for sorting of emulsion droplets with different sizes concurrently flowing in a microfluidic Hele-Shaw channel. The aqueous droplets of varying radii suspended in olive oil are separated into different streamlines across the channel upon interaction with a shallow (depth similar to 700 nm) inclined guiding track ablated into the polydimethylsiloxane-coated surface of the channel with focused femtosecond laser pulses. Specifically, the observed differences in the droplet trajectories along the guiding track arise due to the different scaling of the confinement force attracting the droplets into the track, fluid drag, and wall friction, with the droplet radius. In addition, the distance traveled by the droplets along the track also depends on the track width, with wider tracks providing more stable droplet guiding for any given droplet size. We systematically study the influence of the droplet size and velocity on the trajectory of the droplets in the channel and analyze the sensitivity of size-based droplet sorting for varying flow conditions. The droplet guiding and sorting experiments are complemented by modeling of the droplet motion in the channel flow using computational fluid dynamics simulations and a previously developed model of droplet guiding. Finally, we demonstrate a complete separation of droplets produced by fusion of two independent droplet streams at the inlet of the Hele-Shaw channel from unfused daughter droplets. The presented droplet sorting technique can find applications in the development of analytical and preparative microfluidic protocols.