x2Detention Gas
As long as this Pokémon is your Active Pokémon, put 1 damage counter on each of your opponent's Basic Pokémon between turns.
Splattering SludgeThis attack does 20 damage to each of your opponent's Benched Pokémon that has any damage counters on it. (Don't apply Weakness and Resistance for Benched Pokémon.)
If Weezing has 10 HP left and is Poisoned, would it be Knocked Out before its "Detention Gas" Ability takes place?
No. Even if a Pokemon receives more damage counters from Special Conditions, Abilities, etc. than its remaining HP, that Pokemon isn't Knocked Out until "between turns" is over.
My Active Pokemon got Knocked Out between turns because it was poisoned and Weezing now becomes the Active Pokemon; does its "Detention Gas" Ability work?
No, because you wouldn't replace your KO'd Pokemon until the between turn phase is over. When Weezing comes up, it's too late for Detention Gas at that time.