Why is it easier for me to walk along a balance beam with my arms extended on either side of me than if I simply allow my arms to hang limply at my sides?
Similar reasons to why figure skaters spin faster when they pull their arms into their bodies. I’m sure a physicist might be able to offer a more detailed explanation of moment of inertia, but this link is similar to what I remember learning in physics.
BTW, if you don’t see the connection, think of the spot where your feet touch the balance beam as the “pivot,” similar to the point around which the skater spins.
You are using your arms for added balance. How does this work? When you extend your arm, you are placing a mass away from your center of gravity so that you can use it for correction. Suppose you were about to fall to the right; you would lower your right arm which would push you back upright. The same idea applies to the big sticks tightrope walkers carry, except that the sticks are much better (heavier and longer).
With your arms stretched out to the side, you can change your center of gravity with a smaller movement of the arms than if they were by your side. Changing your center of gravity is how you get back on balance when you start to fall off.