A pinching-antenna system (PASS)-enhanced mobile edge computing (MEC) architecture is investigated to improve the task offloading efficiency and latency performance in dynamic wireless environments. By leveraging dielectric waveguides and flexibly adjustable pinching antennas, PASS establishes short-distance line-of-sight (LoS) links while effectively mitigating the significant path loss and potential signal blockage, making it a promising solution for high-frequency MEC systems. We formulate a network latency minimization problem to joint optimize uplink PASS beamforming and task offloading. The resulting problem is modeled as a Markov decision process (MDP) and solved via the deep reinforcement learning (DRL) method. To address the instability introduced by the $\max$ operator in the objective function, we propose a load balancing-aware proximal policy optimization (LBPPO) algorithm. LBPPO incorporates both node-level and waveguide-level load balancing information into the policy design, maintaining computational and transmission delay equilibrium, respectively. Simulation results demonstrate that the proposed PASS-enhanced MEC with adaptive uplink PASS beamforming exhibit stronger convergence capability than fixed-PA baselines and conventional MIMO-assisted MEC, especially in scenarios with a large number of UEs or high transmit power.