Dredging up this thread again, here is another approach to building a box that is strong and light.
Cut the sides and bottom from 1/8" luan plywood, paneling or something similar. The cuts do not need to be perfect. Tape the pieces together on the outside to make a box. I used a few pieces of masking tape.

Mix up some resin with a thickener to get something with the consistency of cake frosting. Use wood flour as a thickener if you intend to have a natural wood finish. Otherwise use a something like cabosil (silica powder). Apply the thickened resin to the inside corners to make a smooth fillet.

Let the resin start to set up, but before it gets hard lay strips of fiberglass tape (fiberglass cloth with a selvage edge) along the seams.

Wet the fiberglass out with neat (not thickened) resin. After it is wet out, the fiberglass will almost disappear.
It is possible to do this with polyester resin but epoxy resin is easier and safer to work with and will give you a longer pot life before it sets up.

You can epoxy a piece of nylon strap or webbing to the top and bottom to make a very strong, cheap, and non-corroding hinge. You will probably have to glue one side and clamp it while it dries, then glue the other side,

Finally, coat all the rest of the wood with resin to make sure the wood never gets wet. Then start sanding, smoothing and fairing to get a satisfactory finish. I hate this part and am willing to accept some runs or bumps.
Epoxy resin needs UV protection. You can varnish it with polyurethane to maintain the appearance of the wood, or paint it.

You'll be surprised how strong the box is. I can stand on this one. If you want it to be stronger, do not use thicker wood, add more fiberglass reinforcing. It is possible to embed fiberglass or carbon fiber fabric on the outside too, but it's tricky because the fabric will want to lift up along the edges before the resin dries. It can be held down until it dries by wrapping with plastic or peel ply or by vacuum bagging it. It's easier to just put the reinforcing fabric on the inside.

I have started fishing from a different canoe and my old Pelican tackle box won't fit anywhere. This little box has a sloped bottom so it will fit into an oddly shaped spot on the foredeck where I can reach it. It holds a rain shirt, cap, extra jigs, leader material, reel oil, pliers, etc. Make the box to fit the need.
-steve