The propagation of (2+1)D paraxial symmetrical hyperbolic secant beams in weakly nonlocal nonlinear media is studied by variational approach. A series of differential equations which describe the evolutions of the width, the phase, the phase front curvature, and the amplitude of the beam are obtained. The critical power for a beam propagating as a spatial optical soliton in weakly nonlocal nonlinear media is also obtained. A quantitative depiction of the steadying effect of nonlocality on the propagation of a beam is obtained through the steadiness analyse, which provides a self-consistent explanation of the transition from unsteady local kerr solitons to steady weakly nonlocal solitons. The results of numerical method agree with that of variational calculations, implying that hyperbolic secant function is a good approximation to a (2+1)D weakly nonlocal spatial optical soliton.