the solubility of the carbonate and sulphates of the group 2 is decreases down the group due to the constant lattice energy and the decrease in the hydration energy so why the solubility of the carbonates and the sulphates of the group 1 increases down the group

Solubility is based on 2 factors. lattice energy and hydration energy.
lower the lattice energy , higher the hydration energy , greater is the solubility.
In general, when the size of the ions is similar, solubility is less. In group 2 as we go down , size becomes similar. Thus decreasing the solvation. On the contrary , in group 1, size mismatches due to the presence of 2 cations. Thus it increases as we go down.