Robotic blimps, as lighter-than-air (LTA) aerial systems, offer long endurance and inherently safe operation but remain highly susceptible to wind disturbances. Building on recent advances in moving mass actuation, this paper addresses the lack of disturbance-aware control frameworks for LTA platforms by explicitly modeling and compensating for wind-induced effects. A moving horizon estimator (MHE) infers real-time wind perturbations and provides these estimates to a model predictive controller (MPC), enabling robust trajectory and heading regulation under varying wind conditions. The proposed approach leverages a two-degree-of-freedom (2-DoF) moving-mass mechanism to generate both inertial and aerodynamic moments for attitude and heading control, thereby enhancing flight stability in disturbance-prone environments. Extensive flight experiments under headwind and crosswind conditions show that the integrated MHE-MPC framework significantly outperforms baseline PID control, demonstrating its effectiveness for disturbance-aware LTA flight.