Type is a distinct quality of weapons, but a variable set of attributes for armor. Weapons are always one Type; Armor give protection against each of three of the Types that remains the same value from the time it is dropped, found, or forged. The three Types are Blunt, Edged, and Piercing.
Entities' resistance to damage type varies between the three types so much that it is arguably quite effective, and certainly much easier, to keep only three weapons on hand, one of each Type of damage, and target the enemies' weaknesses in this regard instead of using Class or Affinity. There are a few exceptions, notably Rosencrantz, Deaths, and the final boss, where there is no advantage to using one Type over another, and where there is some elemental weakness or the obvious Class weakness.
Type bonuses of armor vary from piece to piece; it is thus advantageous to forge armor from stronger pieces. For example, Armets drop and are usually found at 4/6/4 (Blunt/Edged/Piercing). A 19/19/19 Armet can be made by combining a Tilt Glove, with its 12/12/12 bonuses, with a Missaglia, also 12/12/12.
Type bonuses combine with formulas very similar to affinity bonuses. Bonuses are added together and multiplied by a percentage. The more similar the equipment ingredients are, the better the bonus, as in the example above. Similar materials, same equipments, and similar bonuses are multiplied by higher percentages.
Armor is immensely more difficult to maximize than weapons. It is very hard to overstate this; Weapons can be maximized by beating on dummies to get their affinities and class. Even that job is arguably more difficult to achieve with armor, but there is a whole other variable statistic on armor that comes ready-made on weapons: Type. Maximizing Type on armor multiplies the difficulties of obtaining weapon blades by multiples of ten or even a hundred, depending on the recipe. Maximizing is not necessary to complete the game, and in fact it is less effective at the primary purpose of damage reduction (not dying) than Affinity is, inasmuch as the most dangerous killers in Vagrant Story tend to be spellcasters. On the other hand, Resists are much more powerful against physical attacks than merely higher Tiers of armor, which in turn are better than higher Materials.