Every melee attack has certain base damage, skill based bonus damage and also damage from the weapon. 
General logic is that some weapons such as swords require more skill, so they start with lower damage and scale better with skill, while weapons like maces and spears are easier to use and thus more efficient in the beginning but they scale less with skill.

daggers / throwing knives / swords:
cut: 40 base damage + (skill * 0.53) + weapon cut damage
pierce: 50 base damage + (skill * 0.46) + (weapon pierce damage * 10(thrust modifier) * 0.2)

two handed swords:
cut: (40 base damage + (skill * 0.53)) * 1.3 + weapon cut damage
pierce: (50 base damage + (skill * 0.46) + (weapon pierce damage * 10(thrust modifier) * 0.2)) * 1.3

one handed axe / throwing axe:
cut: 60 base damage + (skill * 0.4) + weapon cut damage

two handed axe:
cut: (60 base damage + (skill * 0.4)) * 1.3 + weapon cut damage

one handed maces:
pierce: 40 base damage + (skill * 0.4) + weapon pierce damage * 10(thrust modifier) * 0.2
blunt: 30 base damage + (skill * 0.13) + weapon blunt damage

two handed maces:
pierce: (40 base damage + (skill * 0.4) + weapon pierce damage * 10(thrust modifier) * 0.2) * 1.3
blunt: (30 base damage + (skill * 0.13)) *1.3 + weapon blunt damage

one handed polearms:
cut: 50 base damage + (skill * 0.46) + weapon cut damage
pierce: 60 base damage + (skill * 0.26) + weapon pierce damage * 10(thrust modifier) * 0.4

two handed polearms:
cut: (50 base damage + (skill * 0.46)) * 1.3 + weapon cut damage
pierce: (60 base damage + (skill * 0.26) + weapon pierce damage * 10(thrust modifier) * 0.4) * 1.3

couched lances and spear bracing:
couched skill = 0.5 + skill * 0.0225
skill cap = 100 + skill * 1.3
if weapon weight is lower than 1.5 kilo (1 handed spears used by infantry), weight of the weapon in calculation is increased by 0.5 kilo

ballistic damage = relative lance speed * relative lance speed * 0.5 * weapon weight
couched damage = relative lance speed * relative lance speed * 0.5 * (weapon weight + couched skill)
if couched damage is higher then skill cap then couched damage = skill cap
if ballistic damage is higher than skill cap then couched damage = ballistic damage
if couched damage is higher than 430 then couched damage = 430 (breaking point of ash lance handle is roughly 430 joules).