It looks like you are studying the peroidic table. Same Anions differing cations.
Ba,Sr,Ca,Mg is the way they line up on the periodic table. Based on electonegativities The Mg should be more soluble in water than would be Barium salts.. Also The position of Magnesium is close to sodium.. General rule of thumb all sodium salts are at least somewhat soluble in water.
Solubility of iodate (g/100ml) at 20 degree celcius Mg-iodate 8.6 Ca-iodate 0.24 Sr-iodate 0.19 Ba-iodate 0.035
The hydration energy values of cations increase with decrease in cation radius and higher the hydration energy higher is the tendecy to go into solution, overcoming the lattice energy. Hence solubility increases from Ba to Mg along the group upward