We investigate model reduction, using balancing methods, of the unsteady aerodynamics of flexible aircraft subject to asymmetric gust excitations. The aeroelastic response of the vehicle, with possibly large wing deformations at trim, is captured by coupling a geometrically-exact beam formulation with the three-dimensional unsteady vortex lattice method. Consistent linearisation of the structural degrees of freedom allows the projection on a few vibration modes of the unconstrained aircraft and permits the vehicle flight dynamics to have arbitrarily-large angular velocities. The linearised aerodynamic system, which defines the mapping between the small number of generalised coordinates and the aerodynamic loads, is then reduced through balanced truncation. Numerical studies on a representative high-altitude, long-endurance aircraft demonstrate the reduced-order modelling approach for spanwise non-uniform discrete gusts over a range of gust lengths and lateral placement.