The approach using the large-M-inequality principle introduced by Acerbi and Mingione has been broadly used in $W1,p-regularity theory for nonlinear equations in divergence form. We apply this approach to determine an alternative proof of the local W2,p-estimate for viscosity solutions to the fully nonlinear equations. Using this method, we derive weighted Hessian estimates in variable exponent spaces for the viscosity solutions when nonlinearity F is assumed to be asymptotically convex.