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.
Source: TPCi Rules Team (2019-06-06)

Relevant cards

Note: All applicable cards may not be listed below.
SM10_74
SM10_74