When Cull the Weak is played, can the opponent use his Hidden Wages of Pain to do 3 damage to the unit he wants to kill with Cull the Weak? Or does Wages of Pain kill that unit and he has to choose a different unit to kill?

Yes, your opponent can use their hidden Wages of Pain to kill a unit in response to Cull the Weak, and this will influence the choice they have to make when Cull the Weak resolves.

The Sequence

1. Opponent plays Cull the Weak: They place it on the chain. It does not target, so no choices are made at this time.
2. Opponent plays Wages of Pain (from Hidden): Since playing from hidden is a [Reaction], they place it on the chain on top of Cull the Weak. As part of playing it, they choose a unit to target.
3. Chain resolves (LIFO - Last In, First Out):
   • Wages of Pain resolves first: It deals 3 damage to the chosen unit. If this damage kills that unit, it is sent to the trash.
   • Cull the Weak resolves second: Now it is time for each player to resolve the instruction "Each player kills one of their units."

Impact on Cull the Weak

Because your opponent's Wages of Pain killed the chosen unit, that unit is no longer available on the board when Cull the Weak resolves.

• If your opponent had another unit remaining, they must choose one of those to kill for Cull the Weak.
• If your opponent had no other units remaining, they perform as much of the effect as possible—which, per the "do as much as you can" rule (Rule 359.3.e.11), means they do not kill any unit for Cull the Weak.

In either case, you are still required to kill one of your own units if you have one available, as Cull the Weak's instruction applies to each player independently.