<p>This paper investigates a perturbed generalized Gardner equation incorporating weak backward diffusion and dissipation effects. Initially, under specific parameter conditions, we derive the exact expression of solitary wave solution for the unperturbed equation by using the dynamical system theory. Subsequently, by employing geometric singular perturbation theory and analyzing perturbations in a Hamiltonian system, we demonstrate that both solitary wave and periodic wave solutions persist for any energy parameter <i>h</i> within a specified interval under small perturbations. Additionally, through the analysis of Abelian integral ratios, we establish that the limiting wave speed <i>c</i>(<i>h</i>) and the period <i>T</i>(<i>h</i>) for these solutions are strictly monotonically decreasing with respect to <i>h</i>. Furthermore, the upper and lower bounds of the limiting wave speed and the period for these solutions are obtained. Numerical simulations are in complete agreement with the theoretical results.</p>