We present detailed studies of ionic conductivity in several polymerized ionic liquids (PolyILs) with different size of mobile ions. Presented analysis revealed that charge diffusion in PolyILs is about 10 times slower than ion diffusion, suggesting strong ion-ion correlations that reduce ionic conductivity. The activation energy for the ion diffusion shows a nonmonotonous dependence on the mobile ion size, indicating a competition between Coulombic and elastic forces controlling ion transport in PolyILs. The former dominates mobility of small ions (e.g., Li), while the latter controls mobility of large ions (e.g., TEST). We propose a simple qualitative model describing the activation energy for the ion diffusion. It suggests that an increase in dielectric constant of PolyILs should lead to a significant enhancement of conductivity of small ions (e.g., Li and Na).