Flight physics for a roll
Typical airplane is not stable in roll. The outside wing flies a bit faster, which does indeed make it produce a bit more lift and that in turn will make it bank into the turn, tightening it and if left uncorrected, ending in a spiral dive.

In a coordinated turn, an aircraft even can't be made stable in roll. There is no way to create a restoring force without involving side-slip. 
The only thing that can be provides is the yaw-roll coupling where a slip produced a rolling moment into the slipping turn. This rolling moment is affected by dihedral and sweep.

Fortunately as the turn tightens, if the rudder is held fixed, some slip does develop that can provide the restoring force reducing the bank. However, it causes another dynamic mode, the Dutch roll.

As the bank increases, the tendency changes from Dutch roll to spiral mode. If you wanted to avoid the spiral mode, the Dutch roll would be very strong, so practical aircraft are designed with moderate yaw-roll coupling and do require a bit of opposite aileron in turns.