I don't think using a hollowed-plywood core is a lightweight method, so I took John's photo and traced out the areas:
So that's 45% of the core that's still present. OK, this is a fairly extreme example, with the completely solid area alongside the galley, but other folks have left even bigger areas not cut out.
So that core plywood still weighs 45% of the full sheet - if it's made from 3/4" ply, it is about the same weight as a sheet of 3/8" ply with no cut-outs. So then add at least 1/8" either side for the skins and the sandwich weighs the same as a solid sheet of 5/8" ply. Other folk have just used a single piece of 1/2" ply - and that is actually lighter, as well as being much simpler.
The plywood core method does allow some insulation to be added, but when 45% of the area is solid ply with no insulation, is this really much of a benefit?
Stick-built sandwiches are definitely the way to go if you want a light wall (if you're not going to the ultimate of a bonded sandwich with foam core), but what you must do is minimise the width of the sticks. As a rule of thumb, I would say the sticks must not be much wider than they are thick, so nominal 1"x1" is OK and nominal 1"x3" is bad.
Incidentally, the stick width needed for structural strength is pretty small. If the sticks are wide enough to be a practical build method (like the 1x1 example) then they're much stronger than they need to be - with 1/8" ply skins, I think 1/8" ply webs
on edge would be strong enough, though that would be near impossible to build.
Andrew