Awkward weapons are… awkward to attack with. They usually heavy or unbalanced, or just badly designed for use in combat.
A weapon’s awkwardness adds dice to the target’s dodge attempts (if any).
A weapon’s awkwardness removes dice from the wielder’s block attempts.
A weapon’s awkward rating removes dice from the next initiative check made after an attack with the weapon (on top of any bonus or penalty from attack maneuver itself).