Having designed and built a lot of paper models, I know a bit about it. Two layers of cardstock (100#) will flutter a lot. It will not be stiff enough. You want to sandwich a piece of thin cardboard (like heavy box material or thin Bristol board) inside. The technique I use is what I call the floating fin core method. Use one piece of 110# card for the outer skin and design it so the two halves fold around the leading edge - this will give you a rounded leading edge. Cut the core so it is about 1/8" smaller than the actual fin - use the same pattern but take 1/8" from the tip and trailing edges, keeping the core flush with the leading edge and the root. Next, you want to glue the core into the fin, but only apply glue to the root edge of the core. Glue the fin closed with glue at the root, tip and trailing edges, and burnish the cardstock down (burnishing helps the white glue grab better). Trim the tip and trailing edge so they are clean (helps to make one side of the fin a bit larger than the other and just trim off the excess). By only gluing the core into the fin wrap at the root, you will avoid a lot of the potential warping. You will still want to press the fin under a heavy book to dry. Another trick to minimize warping of cardstock fins is to lay it out so the leading edge is at a 45degree angle to the long axis of the page - paper has a grain just like wood does and it is usually along the longer axis of the sheet, at least for 110# card. Laying it out at 45degrees means that when you fold the fin at the leading edge, the grain of each side will be 90degrees to the other side.
Hope these tips help!