This was originally intended for the toss-it contest, but it didn't quite fit, I got hung up on the video, and they the local virus swept through the family and I never got around to finishing it. Now that the toss-it contest is over, I can just publish without the video, and maybe it will still be interesting...
This isn't so much plans for a particular paper airplane, as a concept and technique that could be used for a whole new style of airplane, not TOO much more complex or expensive than the typical all-paper airplane.
Step 1: Weighing Paper
Here, we have a regular 8.5x11 inch piece of paper. It weighs about 4.6 grams (Isn't it fun to mix those metric and american units?) If we fold this into a paper airplane, it will still weigh the same (of course), but only PART of the weight will be used in "functional" parts of the plane like the wing surfaces. In fact, in a model like the classic Dart, only about half of the paper will end up in the wings (and a good part of that is folded in multiple layers, so it's not particularly efficiently applied to the wings.