DoT WEAKENING
Essentially, weakening effect works by adding up all the damage done to a mob by DoTs in a single tick. For the remainder of that tick, the mob directly deals less damage in melee based on how much DoT damage it is taking in proportion to its HP.
This effect is intended to add a bit more viability for DoTs in the raid game, as even a percent or two of reduction is a lot on a top end raid mob, but it will also be beneficial in the EXP game and on lower levels, especially since DoTs can shave off quite a few percent of a mob's HP every tick.
The max impact of DoTs are 10% direct melee damage reduction.