The oil pump explained differently.
(I could see possibly confusion in his explanation)
The weight is there to distribute the load over both pump, and return.
On return ( down stroke of the pump to get more oil) the motor that would have been mostly unloaded, is used to lift the weight, which is generally takes somewhat less than the power needed to lift the oil.
As the pump starts to lift oil , the weight then is falling so (most) of the energy the motor used to lift the weight is now being returned, helping the motor lift the oil. The motor then only has a slight harder time lifting the oil than it did the weight.
As Ross points out the weight is only there to balance the load on the motor between cycles.
It does a lot to reduce stress and friction on parts, and without it you would need for double the motor capacity, while using that capacity only half of the time (one of two cycles)
This weight arrangement only increases the efficiency by spreading loads over time/cycles allowing a smaller drive motor and certain parts to be smaller.
Again as Ross said,
every time you add parts, you increase losses, unless its overall effect is to reduce friction.
In this case its only doing that by balancing/distributing load over times of load/no load.
No such thing as a free ride when it comes to energy, sorry.
p.s. I know parts of this may over simplify and not
always be entirely accurate but its a generalization and I'm trying to keep it simple.
Hate to have the oil wrastlers out there rip into me