Statement-I : Solubility of alkaline earth metal carbonates decreases down the group.
Statement-II : Size of anions being larger than cation, lattice energy remains constant while hydration enthalpy decreases.

The ability of alkaline earth metal cations to hydrate themselves decreases down the group due to decrease in charge density.
As the hydration enthalpy decreases on going down the group, the solubility of the carbonates and sulphates also decreases.