Acceleration while climbing a rope Consider a man hanging on a rope. If weight of the body is the maximum force one can apply on a rope, where does the additional force that accelerates the man upwards come from and thus increasing the tension of the rope?
 A: The maximum force that the man hanging can apply is not his weight. The man can use his muscles to essentially  pull the rope down, which will act to increase the tension in the rope (Bc the end of rope is fixed) such that net force on the man is $T_{induced} - mg = ma$. 
If this isn’t clicking for you, imagine you could control the  value of $g$. Decrease the value until it approaches zero so the man is weightless. The problem reduces to, say, a man holding onto a rope attached to a wall on the international space station. Clearly, he can use his muscles to pull on the rope which will increase the tension in it and propel him forward. 
Note, if instead of forces we think in terms of work done, we might ask whose doing the work to increase the gravitational PE of the man climbing up a rope? It can’t be the rope Bc the tension force is never displacing the man (his hand and the rope stay in same spot so $W = F\Delta d = F (0) =0$. The answer is that the man does work on himself. Or more precisely, the muscles are doing work through contraction. 
