Great advice all, and I now realize my use of the word "attic" was
misleading. It's actually a third-floor living space, complete with
full bath, bedroom, etc. so I think the floor will be strong enough.

Good to know that plywood boxes will serve as adequate frames for the
drawers. One question: I like the idea of face frames on the boxes
with an overlay drawer front, but won't a face frame prohibit me from
mounting the drawers slides directly to the sides of the plywood
boxes? Will I need to attach the slides to boards that are screwed/
glued to the insides of the boxes so that the slides will clear the
face frame?

Thanks!

Kevin