I have some 1/16" fins that I want to stiffen with carbon fiber. They are long things like the fins on Big Bertha / Baby Bertha. Does the type of weave matter? From past discussions, I assume it does matter but I can't find any references.
Yes. Stiffness is along the long axis of the fibers. Standard weave fabric is stiff in two directions, unidirectional weave is stiff in one direction and twill weaves are a bit less strong, but the directionality is a bit more spread.
For something like you describe, I'd run a couple layers of unidirectional fabric down the long axis of the fins as well as a layer or two of standard weave in normal orientation. (square to the airframe)
W
I second that. You especially want the part of the fin near the leading edge to be stiff so that when the wind is pushing it sideways, the back edge deflects more than the front edge to keep it from fluttering. You will be surprised at how much stiffer a little bit of unidirectional carbon can make your fins. Soller composites is a great place to get it.