Paper armor, if hardenned correctly is very tough. At around 8 sheets thick it's semi difficult to cut with a knife (like cutting into thermoplastic), at around 16 sheets thick you'll need to really start working away at it. And it is very light weight
I highly doubt that paintball would get through by sheer force, although the wetness from the paint might weaken it. Taping over it would probably help (plus duct tape is awesome).
To harden paper 'correctly', cover a half of the paper in glue, then fold it in half. Cover again the half, and fold. Keep doing this down to desired size. Usually I'll go down to an 1/8 for random projects. For armor I might do 1/16 (starting with normal letter sized paper). I recommend using PVC or Elmers glue, although superglue would work better (downside being mess and you'd have a hard time drying it with having it stick to something). Make sure the glue completely saturates the paper each time, you want a lot in there.
This:
http://www.youtube.com/watch?v=e2wBY-EWW4QIf you want larger sheets, I would fold a paper hot dog style (if with letter paper, then it would be 4.25 by 11). Then I would put a second sheet with one half in it, one half out. It would look like a Z (am I making any sense?). Just keep layering it that way. Folding the edges works the best, non folded edges tend to split apart after a while. Plus folds mean that the paper can't warp or slide as much, since one side is locked down. Use glue as you normally would, between each layer, and liberally.
I know there's paper mache and other things out there, but I don't think they're as tough.
I think something like a vest made like scale maile would be the easiest. Just fold the paper down to 1/32 (I would recommend using two halves of a4 or letter folded down to 1/16, folded into each other to make the 1/32. After 4 folds it gets messy). Dry with a heavy book over it (prevents warping and split edges). Then drill out 2 holes on each corner. String em up and you'd be done. Or you could work with bigger sheets and make a lorica segmentata.
I'm working on a brigandine right now, and I personally wouldn't want to ruin one with paint. It's very time consuming(especially with sizing, if you know how to tailor then it would probably be a lot easier), and I wouldn't want to damage it.