When I fold out of stiffer paper (especially if it is larger) I pre-score the paper along some of the preliminary crease lines. You take a straight edge to line up the crease and then press down with a sharp implement, as if you were drawing a line. Score the paper on the valley fold side - obviously, turn the paper over to produce a mountain on the opposite side. I use a ballpoint pen that has run out of ink, or you could use a butter knife, knitting needle, bone folder, etc., Depending upon the paper, you have to experiment with pressure; paper that is handmade will have more loft and irregularities, therefore may tear, whereas more commercial papers that are rollered, denser and have a more organized matrix can take more pressure.
Question for the origami community: Would you consider scoring the paper "cheating" - like using scissors, tape and/or glue? Technically, you could take a crease pattern, score all of the mountains and valleys, then put all of the folds in place. I think that it's not just the creases that make it an art (although some of the crease patterns in and of themselves are beautiful!) but it's the "make it 3D" component that non-origami folk find magical. One of my most favorite models is the Kawasaki rose; the folding of the preliminary crease lines could be seen as simple (but elegant) however, the forming it into a rose moves it into a non-beginner's model. My other comment on folding with stiffer paper is that I found some paper way back when made for calligraphy that worked well. It was not as stiff as card stock, but had a coating on it (perhaps even methyl cellulose?) that made the surface slick so that the pen would glide over it. To me, it's not just the folding, but finding the right paper for the job that can be the most challenging.
