I've noticed that modern-day cocked hats (i.e. ones worn by re-enactors of earlier time periods) have their brim folds fixed into position by means of narrow twill tape or cord that run through the hat and brim, and are tied off inside, leaving those parallel lines of tape on the outside. Is this the original method of securing the brim, or is that just a re-enactor thing? Or is it more of a military thing, and the owners of fancier, more gently-rolled tricorns would have worn hats that were steam-shaped somehow? I mostly do Native living history, so I guess I never thought too much about cocked hats before.
While cocked hats are blocked and shaped with steam and stiffened with some sort of shellac-like liquid, keeping the brim up does best with some sort of support. Generally this is done by way of cord laced through and tied off inside or by heavy stitches. The nice thing about the cord is that it can be un-laced to allow the brim to be let down for rain protection, etc. You'll often see a cockade, button, or lacing over the area. A cheaper hat will be of wool felt, a more expensive of beaver perhaps trimmed in gold lacings, etc. Just a difference in quality of goods, labor is the cheaper part.