Work done (by gravity) on paired blocks 
Why does gravity do more work on the block going down?
The total work done (by gravity) on the $8kg$ block is more than the work done (by gravity) on the lighter block. How?
 A: The OP and Comments give two opposite answers as correct for this question Here's the one I think is correct:
There is a system, consisting of two blocks connected by a rope.
It is initially at rest, and after a period of time, it (all of its parts) is moving.  It has gained kinetic energy, and therefore work has been done on it by an external force.
Both parts of the system are moving at the same speed, whatever it is.  (It could be calculated, but we don't need to do it)
Since both parts have the same speed, the kinetic energy is divided in the ratio of the masses.  The $8$ kg block has $\frac{8}{14}$ of the kinetic energy.
The trick here is that if you are finding the work done by gravity, you don't count potential energy as well.  You'd be double counting the energy.
Consider a simple pendulum;  From one point of view, no work is done, since the total of PE and KE is constant;  it just swaps back and forth.  
OR
Gravity does work on the pendulum speeding it up on the way down, and the pendulum does work on the earth on the way up.
Either view is correct;  just don't use both...at the same time.
