The role of rare-earth (R) ions on the magnetodielectric (MD) coupling is always intriguing and markedly different for different systems. Although many reports are available concerning this aspect in frustrated 3dtransition 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 ~30 kOe, 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.