Why Cu2+ is more stable than Cu1+ though latter is configurally stable?

Stability in aqueous conditions depends on the hydration energy of the ions when they bond to the water molecules (an exothermic process). The Cu2+ ion has a greater charge density than the Cu+ ion and so forms much stronger bonds releasing more energy.

The extra energy needed for the second ionisation of the copper is more than compensated for by the hydration, so much so that the Cu+ ion loses an electron to become Cu2+ which can then release this hydration energy.