Each weapon consists of a Blade and Grip. The Blade is what does the actual attacking.
There are many different kinds of blades, and they can be made of five different materials -
Bronze, Iron, Hagane, Silver and Damascus. (I don't believe it's possible to have a blade made out
of Leather or Wood - if it is, it happens so rarely as to be unimportant.) Each material has certain modifiers that are applied
to the base statistics of a blade. For example, if you have a Hagane Battle Knife, its STR will
be the base STR (4) plus the material modifier (+6 for Hagane), for a total of 10. Blades can
have one of three types (Blunt/Piercing/Edged), obviously independent of material. They also
have an innate RISK statistic, which determines how much your RISK will increase every time you
attack with that blade.
Your fists also count as weapons, but they are not subject to material modifiers (obviously). Their
power depends only on Ashley's innate statistics, which of course vary.