We explore the methods to achieve an approximately self-foldable crease pattern of flat rigid origami whose motion is driven by gravity. The approximate self-foldability is attempted from the mechanics of the panel-pin model developed for the equilibrium analysis of rigid origami. The predominant deformation mode under gravity is estimated from the total potential energy and the eigenvalues of the stiffness matrix of the model that has small rotational stiffness along the crease lines. The arrangement of the crease lines is optimized by maximizing the gap between the eigenvalues or the total potential energy variation in the direction of the eigenvectors of the stiffness matrix.