I think that weapons should be fit into one of three categories:
Single-handed Weapons - Can only be used in one hand. If other hand is free*, it can be used to do an additional barehand attack (which would NOT get unarmed combat bonuses or train unarmed weapon skill). No bonus for use without additional weapon or shield, but would have lower movement cost for dual-wielding if both weapons are single-handed weapons.
Dynamic Weapons - May be wielded in one hand. If other hand is free, weapon gets a 1.5x bonus with regards to Strength.
Two-handed Weapons - Requires both hands to wield. Gets a 2x bonus with regards to Strength.
Whether the first two categories are split according to weapon type (daggers and knives would always be single-handed weapons), by weight, or be specific to each weapon (a club might be single-handed while a cudgel might be dynamic) is up for discussion, of course.
This gives a little more balance between the options, in my opinion, and encourages players to consider going without a shield, by giving every weapon a potential benefit to fighting without a shield.
* I'm undecided on whether the game should automatically attack with the free hand (could be an issue when, say, attacking a corrosive being with nothing but an eternium dagger), or if it should be limited in some way - either by a tactic (Aggressive or higher causes you to use extra barehand, Normal or lower and you only use the weapon), by a specific command (rather than just moving into the foe - note that this could potentially also be used to do minor damage using a shield in dire circumstances), or as a switch on the equipment screen.