Human Pyramid Are Heavy

Probability Level 4

A human pyramid is built up by several layers. At the top, there is one person, and each subsequent layer has 1 additional person. Each person is supported by the 2 people that are beneath them.

Consider a 9 layer pyramid, which comprises 45 people. Assuming that all the cheerleaders weigh 128 pounds each, and that the weight is equally distributed amongst both supporters, what is the most weight supported by anyone in this pyramid?

How would you generalize this?

Image credit: Wikipedia Pere Lopez