In Dynamis, almost all enemies can be staggered, even standard non-NM mobs. Doing so will cause enemies to drop ancient currency more frequently, as well as open more potential drop slots for currency to drop.
In order for a player to trigger weaknesses, they must have obtained at least 3 of the 5 available time extensions in the zone on their current visit. Obtaining more will increase the chances of staggering enemies, as well as increase both the drop rates on ancient currency and the negative effects on the staggered enemy:
0-2 ~> None
3 ~> Low proc rate / Blue - Potentially transient Amnesia, or nothing.
4 ~> Medium proc rate / Yellow - Terror/Stops 2-Hour/Able to Re-use 2-Hour
5 ~> High proc rate / Red - Terror/Stops 2-Hour/Unable to Re-use 2-Hour