I find this an interesting discussion but also a bit academic. What I mean is, it doesn't matter much for practical applications.
If the definition of "efficiency" above is correct ( and I like it) than heaver bows are almost certainly less efficient. Does of course depend on bow design, arrow weight, correct spine...
BUT, 100# war bow at 60% efficiency (let's assume it is roughly a poundforce of 60) will still be impacting more than a 50# bow at 90% efficiency (pound force 45). Not very efficient for the heavy bow, but definitely more punch.
I think what was said above defines efficiency at the point were the arrow leaves the string.
That doesn't cleanly translate into what happens at the target: arrow design, correct spine and distance come into play.
Also, depends on kinetic energy and momentum, and those are two different things that shouldn't be confused.
Practically, it isn't that important and bow choice is more of a case of what you need ( and what you like shooting).
A 50# bow with good efficiency will go through a deer at 20yard. If you try to penetrate chain mail at 50 or 100 you probably need something a bit heavier, "efficiency" be damned.