Right now, there are a few traits boosting a champion's capabilities with certain weapons, but they're just damage boosts - they don't really accentuate the unique properties of each weapon type.  So I came up with a few example traits demonstrate what I'm thinking - these traits would require that the champion have a weapon of that type equipped to be available, and would NOT require a certain path to be selected (with the possible exception of staffs)

Sword:  +1 counterattack/round

Spear:  +1 range (can attack a foe 2 tiles away)

Staff:  Casting a spell during a round gives champion +9 initiative until their next round

Hammer:  Bypass 50% of opponent's armor

Dagger:  +1 crit/level

Bow:  Opponent's move reduced by 1 for their next turn unless they resist

Create enough traits like these, and you could really regard a champion as being a master of a certain weapon.