Lifting small objects at very low speed
First, let's look at the power requirement.  7 kg on earth weighs about 70 N.  That times 6.6 mm/s is only half a Watt.  There will be friction and other effects to make things harder at the motor, so I'd get about a 2 W to motor.

You want a travel of 2 m from a cable.  That probably means the cable unwinding and winding onto a drum that is rotated by the motor.  If you can have a second cable on the same drum winding opposite with a 7 kg counterbalance on it, the power requirments and wear on parts of the system will go down dramatically.

You will need gearing no matter what, so start by looking for a suitable motor and add gearing to reduce its speed.  A lot of motors are available with "gear heads" already built on.  You have some flexibility on the diameter of the drum, so should be able to accomodate a wide enough range to find a gearhead motor that does what you want, or find or make a reduction gear train to add to a bare motor.