Accurate computer simulations of the rotational dynamics of linear molecules solvated in He clusters indicate that the large-size (nano-droplet) regime is attained quickly for light rotors (HCN, CO) and slowly for heavy ones (OCS, N$_2$O, CO$_2$), thus challenging previously reported results. Those results spurred the view that the different behavior of light rotors with respect to heavy ones - including a smaller reduction of inertia upon solvation of the former - would result from the lack of adiabatic following of the He density upon molecular rotation. We have performed computer experiments in which the rotational dynamics of OCS and HCN molecules was simulated using a fictitious inertia appropriate to the other molecule. These experiments indicate that the approach to the nano-droplet regime, as well as the reduction of the molecular inertia upon solvation, is determined by the anistropy of the potential, more than by the molecular weight. Our findings are in agreement with recent infrared and/or microwave experimental data which, however, are not yet totally conclusive by themselves.