We experimentally observed an accumulative type of nonlinear attenuation and distortion of slow light, i.e., Rydberg polaritons, with the Rydberg state |32D5/2) in the weak-interaction regime. The present effect of attenuation and distortion cannot be explained by considering only the dipole-dipole interaction (DDI) between Rydberg atoms in |32D5/2). Our observation can be attributed to the atoms in the dark Rydberg states rather than those in the bright Rydberg state, i.e., |32D5/2), driven by the coupling field. The dark Rydberg states are all the possible states in which the population decaying from |32D5/2) accumulated over time, and they were not driven by the coupling field. Consequently, the DDI between the dark and bright Rydberg atoms increased the decoherence rate of the Rydberg polaritons. We performed three different experiments to verify the above hypothesis, to confirm the existence of the dark Rydberg states, and to measure the decay rate from the bright to the dark Rydberg states. In the theoretical model, we included the decay process from the bright to the dark Rydberg states and the DDI effect induced by both the bright and dark Rydberg atoms. All the experimental data of slow light taken at various probe Rabi frequencies were in good agreement with the theoretical predictions based on the model. This study points out an additional decoherence rate in the Rydberg-state electromagnetically induced transparency effect and provides a better understanding of the Rydberg-polariton system.