The stability of ${\text{Cu}}^{2+}$ is more than ${\text{Cu}}^{+}$ salts in aqueous solution due to:

Although removing the second electron from Copper requires more energy (as ${\text{Cu}}^{+}$ has a stable $d^{10}$ configuration), ${\text{Cu}}^{2+}$ is more stable in aqueous solution. This is because the hydration enthalpy of ${\text{Cu}}^{2+}$ (which has a higher charge density) is much more negative than that of ${\text{Cu}}^{+}$, which more than compensates for the high second ionisation enthalpy.