Once you complete the first "Investigate X" campain task, a couple of things happen. First you get a quest (this one is For Gyrion, the Nostura one is similar and I assume the Kabal one is too).
Also, at the same time, the "Resist the Rituals" and "Secure the District" task rewards change - you get an additional drop:
If you open the Ornately Carved Box, you get a choice of portal stones, corresponding to those "Investigate X" tasks you have completed.
In this case I only get the Abolethic (Gyrion) stone, as that is the only one I have unlocked on the Live server. When I use the stone, I get the "Behind the Mask" quest again.
What does not happen, however, once you complete the "Investigate X" task is the unlocking of the weekly - I had sort-of assumed it would, but maybe you need to unlock a "Confront X" task for that.
Here is the weekly from Preview - I will assume it is the same on Live