The stability in aqueous condition depends on the hydration energy of the ions when they bond to the water molecules. And, the hydration energy is the amount of heat released as an ionic substance is dissolved and its constituent ions are hydrated or surrounded by water molecules.

Now, in Cu²⁺ and Cu⁺ ion, Cu²⁺ has a greater charge density than the Cu⁺ ion and so forms much stronger bonds releasing more energy. Therefore, in an aqueous medium, Cu²⁺ ion is more stable than Cu⁺ ion. This is because the energy required to remove one electron from Cu⁺ to Cu²⁺, is compensated by the high hydration energy of Cu²⁺.