As we move down the group, the lattice enthalpy of carbonates remain approximately the same. Carbonate ion is so large that relatively small changes in the size of the cation do not make any difference.
The solubility of carbonates of alkaline earth metal decreases down the group mainly due to decreasing hydration enthalpies of the cations from Be2+ to Ba2+ .
All the carbonates of alkaline earth metal are more soluble in the presence of CO2 due to the formation of corresponding bicarbonates.
CaCO3 + CO2 + H2O —> Ca(HCO3)2