<p>In this article, we investigate the third-order, fourth-order, and fifth-order weighted essentially non-oscillatory limiters with adaptive linear weights (ALW-WENO limiters) for the same-order Runge-Kutta discontinuous Galerkin (RKDG) methods to simulate hyperbolic conservation laws on structured grids. We adopt the new modified KXRCF shock detection technology to mark the troubled cells and design three new ALW-WENO limiters in the finite element framework on structured grids. The procedures of three new ALW-WENO limiters are designed in these aspects: they always reconstruct one high degree polynomial which is the DG solution and one zeroth degree polynomial which is the cell average of the DG solution, automatically adjust only two linear weights with a new condition, compute two new smoothness indicators, compute two new nonlinear weights, obtain the new polynomial in a WENO manner, and finally modify the degrees of freedom of the DG solution on the troubled cell. It is the first time to use only two unequal degree polynomials to design arbitrarily high-order WENO limiters. The primary benefits of new ALW-WENO limiters mentioned above are their simple reconstruction procedures in the finite element framework and the ease of achieving the arbitrarily high-order accuracies in multi-dimensions. In comparison to previously third-order, fourth-order, and fifth-order MR-WENO limiters which required three, four, and five unequal degree real/ghost polynomials, respectively, it is the first time to always use only two unequal degree real polynomials for obtaining arbitrarily high-order accuracies from now on, respectively. These RKDG methods with novelly same-order ALW-WENO limiters show the good efficiency in preserving the optimal high-order accuracies in smooth areas while compressing the spurious oscillations in non-smooth areas, since they could save about 15%-76% CPU time than that of the same-order RKDG methods with original MR-WENO limiters.</p>