...The outside edge of the beam, furthest from the neutral point is where tension and compression are the highest...
This part of your statement is correct. It is the extreme fibers that take most of the load. Hence the thicker the beam, the stiffer it gets.
A hollow form OF THE SAME WEIGHT will be stiffer because the extreme fibers will be farther apart. However the inner fibers, the "core" keep the extreme fibers from collapsing.
