Maybe I can help you guys with the solution (I'm a mathematician).
As the monkey pulls on the rope to climb up.. the tension in the rope increases by some positive quantity. Regardless of the actual value of this tension (since it would of course vary depending on how rapidly the monkey ascended the rope) the solution is the same. The increased tension from the monkeys pull will be exerted equally on both masses.. since tension of any rope is of course the same at both "anchors". Since the weight is the same as the monkey's weight, both will upwardly accelerate at exactly the same rate. hence, every inch the monkey climbs upwards, the weight will also climb upwards an inch, lowering the rope on the monkey's side one inch rendering the monkey motionless!
Hope this makes sense. The answer is "stays in the same place".
If you need any other help, just go ahead and ask.
I'm trying to apply for OCS aviation slot.. but god my GPA is bad (2.9) so I am hoping a total obliteration of the ASTB will get me in!