6V DC Motor Overheat
I am assuming this is a permanent magnet, brush DC motor. The motor current increased rapidly with a 1 volt increase. 5 volts at 1 amp to 6 volts at 2.3 amps under no load conditions. Typically, the motor current and motor voltage are more linearly related under no load conditions.

The motor, most likely, has bearing damaged and brush or commutator damage.