As I mentioned yesterday, the word jacket also has its origins in Hebrew. Horowitz points out that the English word jacket derives from the French jacquette. Jacquette is a diminutive of the common French name Jacques, which was used to refer to Frenchmen in general, and Horowitz mentions that the jacquette was worn by French soldiers and peasants. Jacques is the French version of the English Jacob, which of course derives from the Hebrew Yaakov יעקב.
Stahl presents another theory where the name Jacques and Jack actually derives from John (which comes from Yochanan יוחנן). John became Jack via the nickname Jankin, but as often happens in both Hebrew and English, the middle letter "n", dropped out in time.
Stahl presents another theory, also mentioned in the Online Etymology Dictionary:
possibly associated with jaque (de mailles) "short, tight-fitting coat," originally "coat of mail," from Sp. jaco, from Ar. shakk "breastplate."
Stahl points out that the Arabic root is שכה - I assume related to the root סככ - meaning to cover.
In German jacket was known as Jacke. Stahl explains how this later became the nickname for German Jews - yekke. The German Jews adopted Western dress before the Eastern European Jews, and this included shorter jackets than were previously worn. Originally this term was derogatory, but after the Shoah, it was not viewed appropriate to call Jews from Germany "German", the way Jews from other countries were called (Russians, Moroccans, Yemenites). From that point the term Yekke lost its derogatory edge.