Some folks like to fill the gaps with balsawood, which provides good, rigid support without adding much weight.
For my builds, I do cut out large areas (I cut all the way through) and then I affix a piece of 1/64" birch plywood, which serves as a surface to mount the weight on, and also stiffens up the entire chassis.
I do the same with 1/64 plywood. or monocate. I have stopped going all the way through i like the stiffness of leaving the top hole.