The role of rare-earth (R) ions in magnetodielectric (MD) coupling is always intriguing and markedly different for different systems. Although many reports are available concerning this aspect in frustrated 3d-transition metal oxides, no such reports exist on higher d (4d/5d)-orbital based systems due to the rare availability of highly insulating 4d/5d systems. Here, we systematically investigated the magnetic, dielectric, ferroelectric, and magnetodielectric behavior of the 6H-perovskites Ba3RRu2O9 for different R-ions, namely R=Sm,Tb, and Ho, which magnetically order at 12, 9.5, and 10.2 K, respectively. For R=Tb and Ho, the temperature- and magnetic-field-dependent complex dielectric constant traces the magnetic features, which manifests MD coupling in this system. A weak magnetic-field (H) induced transition is observed for ∼30kOe, which is clearly captured in H-dependent dielectric measurements. No MD coupling is observed for Ba3SmRu2O9. The MD coupling is enhanced by a factor of 3 and 20 times for R=Tb and Ho, respectively, when compared to that of the Nd-counterpart. These results evidence the gradual enhancement of MD coupling with the introduction of heavier R-ions in this series, which is attributed to their larger moment values. Our investigation establishes dominating 4d(Ru)−4f(R) magnetic correlation in this series for the heavier R-members.