Your hero weapons, and only your hero weapons, evolve whenever you open one of the "core" chests in the Road to Rule, namely Might and Guile (other weapons evolve based on conditions placed on each weapon). Opening each of those chests will evolve your weapons by one "level" and change their appearance.
It should be noted that opening the Magic core chest will not affect your weapons as such, but rather will cause glowing blue (if good) or red (if evil) lines to appear on your body.
Also, the manner in which the weapon changes depends on your previous actions. For example, if you gave lots of gold to beggars, then your weapons will appear golden.
More in-depth guides can be found here and here.
Hope this helps!