well there are quite a lot of different multi use printers out there for you to look at for design inspiration.

The main issue you face is how large a drill/motor you want to use for the cnc side of things.
Weight on the bed isn't as big an issue as you think. If you havea double z screw design with 2 guide rods at each end and maybe one at each side as well. Then the bed will stay stable with an awful lot of weight on it.
Also you'll be using 2 steppers in parallel, which doubles the lifting capacity.

Most multi use machines use a very small cnc head - often an adapted dremel type rotary tool.

Looking at the video - no reason you couldn't stick an extruder and hot end on that machine.

It kind of depends on which side you want the emphasis to be on: cnc or 3d printing.