The Conductivity of Electrolytes based on structure of Ionic Crystal
It turns out, according to this paper, stated:


  The solvent-berg model which put forward the suggestion that smaller ions are strongly interacting with the nearest neighbour shell of solvent molecules. This was considered to be particularly true of cations since these are generally smaller in size than the corresponding anions and have a higher charge density. The ion essentially carries this shell of solvent molecules long enough that this leads to a larger effective diameter which lowers its conductivity to a value smaller than the conductivity of larger ions which have no strongly attached shells of solvent.


And in terms of drag from the polarity of the solvent, namely water, they showed a formula for dielectric friction:

ζDF = 3qi2(ε0 − ε∞)τD/(cri3(2ε0 + 1)ε0)

Where:
ζDF is the dielectric friction,
ri and qi are the radius and charge of the ion, 
ε0 and ε∞ are the static and high frequency dielectric constants of the solvent, 
c is the product of the limiting ionic conductivity and viscosity of the solvent, 

So, I assume that the ionic radius will play a role in its drag by the surrounding polar solvents which will affect its mobility, and therefore the conductance.