Yes, epoxy will make the plane HEAVY. It's a pain to mix, a pain to apply, and a pain to clean up. You'll have epoxy glopped on and stuck to everything.

You can, in fact, assemble a plane using only medium CA, with epoxy for joining the wings and gluing on the tail surfaces. One 1oz bottle should be more than enough for a plane that size. Remember, a little dab'll do it.

CA is different from "Super Glue" or "Krazy Glue." First off, it's cheaper. Second, it actually works.

If you want, plain yellow carpenter's glue is also perfectly fine for assembling planes. It just takes a little longer.