To expand on the two posts above:
1) Baltic birch is great but is heavier than standard "cabinet grade/hardwood" plywood. If you buy "cabinet grade/hardwood" plywood, try to get poplar core. It is stronger, lays flatter and the plies won't separate like fir core plywoods will.
2) One advantage of baltic birch is that it often comes in 5/8" thickness (or the metric equivalent anyways) whereas hardwood plywood normally comes only in 1/4", 1/2" and 3/4". The 5/8" is strong enough for tops.
3) If you go three drawers wide to save weight on the top panel, the added vertical side panels, drawer parts and slides will end up adding as much weight as you saved . . . but you'll end up with smaller, less useful drawers.
4) Torsion box construction has the potential to be lighter. However, this construction method results in thicker panels which use up valuable space.
5) Glue with screws, rabbets, dadoes, tenons etc are your friend. Butt joints with pocket screws are fast but are the very weakest.
6) Rather than turning panels into swiss cheese, I like to route out (relieve or hollow out) areas which are not structural but I don't route all the way through.