|Any fool can be uncomfortable, 'tis a wise man what wears a knitted cap...|
Captain Roger Gary and Lieutenant Michael "Caracticus" Hussey
laud the virtues of the knitted cap during a spring scout.
Virginia shipped a quantity to the Continental Forces, presumably received by Muhlenberg's Brigade (1st, 5th, 13th Va Regt, Continental Line and the 1st and 2d Virginia State Regiments, and the German Regiment), according to Washington's General Orders and a letter to to the Brigadier.
Excellent examples of extant knitted caps and reproductions can be found here:
His very cool Voyageur living history blog by the same gentleman can be found here:
...and my favorite,
From Diderot's Plates,
Only Figures 14 and 15 appear to show knitted caps.
 Journals of the Continental Congress 1774-1789, Vol IV, 1776. 46.
 Hogarth, W (1747) The Idle Prentice, London. http://www.britishmuseum.org/explore/highlights/highlight_objects/pd/w/hogarth,_the_idle_prentice.aspx
 Wallet and Purse Maker." The Encyclopedia of Diderot & d'Alembert Collaborative Translation Project. Ann Arbor: MPublishing, University of Michigan Library, 2010. <http://hdl.handle.net/2027/spo.did2222.0001.396>. Trans. of "Boursier," Encyclopédie ou Dictionnaire raisonné des sciences, des arts et des métiers, vol. 2 (plates). Paris, 1763.