Found an old post that guess into super deep detail about damage calculations. There was another one that was a little bit simpler I remember seeing a while ago, bit I couldn’t find it. I’ll try to give you a bit if an answer though. The calculations for damage on hit are very complex, but essentially: empower increases your Power stat in damage calculations, and Power increases the base damage of a weapons type by that amount (every weapon type in game, gauntlet, sword, staff, etc, has a specific base damage used for all calculations. For example, If your weapon type has a base damage of 60, and your power is at 100, that weapons base damage is now 160. This value is then increased by all of your other affixes and stats in various ways. Weaken affects enemy resistances, which are calcuted at the very end of damage calculations. So, I think it kinda depends on your build, but I Believe Weaken would generally be more effective simply because it is a higher percentage per affix.
I don’t haver time right now, but I will try to do some testing tonight too get more exact figures on the differences.