If you soak a brown paper bag in a glue/paste type of mix this will add a lot of weight. The simple solution is to insert one CF arrow shaft through the center of the wing at roughly 25% of the chord. I have seen this done on a handful of planes and the wings are still together with VERY VERY little weight added.
Actually the glue solution, if diluted and spread rather than just gobbed on full strength, adds very little weight compared to the paper itself. As you say, adding a lightweight spar is a good, light alternative, but you still have to add covering -- to deal with torsion of for no other reason, so the lightness of the spar can be misleading. It has to have the weight of the covering added to it before it can be compared with the weight of the shell of a composite wing. So the paper bag method is probably not as bad as you might first guess... and after all, it is what the original post was asking about.
In the end, it's all good -- it'll work either way and as long as it's done neatly, the weight penalty will be small enough that you can live with it.