There are three primary values which affect the attack strength of a character: damage, to hit value (THV) and hit speed. Damage is self-explanatory. Chance to hit the enemy is 100% / (DV/THV + 1), where DV is the enemy's dodge value, which is calculated from agility, size, burden state, etc. THV also affects the chance to hit weaker bodyparts like the head and the ability to block attacks. How many attacks you can do in a certain amount of time is proportional to hit speed. A skill bonus of X percent increases each by X%.

Conclusion: Weapon skill is very important in combat, but no one can know exactly how much. Personally, I never use the above formulas, but depend on my gamer's intuition.