bcaiko
Emperor
The problem is that the AI has practically infinite happiness in Civ V in order to give it a leg up against the player. War weariness would only hurt the player and in the most annoying way possible.
This is absolutely correct. War weariness would ultimately only effect the player. Especially on higher levels.
The solution to the OP's problem is not to complicate things with a new mechanic, but to correct the AI's peace negotiations calculation.
Just make offering a peace treaty lower war weariness in your cities, and then the mechanic makes sense. You're fighting a war, war weariness is forcing down troop morale/etc., you can offer peace. If the AI takes it, war over and weariness gone. If the AI doesn't you lose some weariness. Further, refusing peace after like 20 turns of war increases the penalties.
In that case, I'd just spam rediculous peace offers where I demand everything they can give me.
"What? I offered you peace. My people aren't getting weary. You should take my rediculous offers."
Given the AI's peace negotiation tactics, the AI will do about the same.