From what I understand, when a god kills another god he gets their portfolio.
Wouldn't this mean that when Cyric killed Mystra he should have just gotten her portfolio over magic, spells, and the Weave?
In the Forgotten Realms Campaign Guide (page 50) of the 4th edition one can read (emphasis mine)
Most scholars believe that the Spellplague was the direct result of the murder of the goddess Mystra at the hands of Cyric, which Shar engineered. This popular theory holds that magic was bound so long in Mystra’s Weave that, when the goddess died, it spontaneously and ruinously burst its bonds. Areas of wild magic, already outside the constraints of the Weave, touched off first, but the plague raged on and on in ever-widening spirals, devastating some places and leaving others untouched. It even tore through the realms of demons, gods, and lost souls before the end.
Mystra seems to be the only one capable to rule the Weave, as reported here\$^1\$: once the goddess was assassinated, the Weave was out of control and then it could burst and the Spellplague took place.
Moreover, Mystra assassination was planned by Shar: the adventure The End and the Beginning\$^2\$ explains that (emphasis mine)
When Cyric murdered Mystra at Shar’s urging, it resulted in the destruction of Dweomerheart, the collapse of the Weave of magic, and unleashed the Spellplague. Although nearly everyone, including Cyric, believed Mystra to be utterly destroyed, in fact her essence was captured by Shar and hidden away in the Towers of Midnight. Ever since the Year of Blue Fire, Shar has been attempting to use Mystra’s essence to forge a new Shadow Weave. Had this plan succeeded, Shar would have assumed the portfolio of the Goddess of Magic and been able to reshape reality according to her whims.
Hence, Cyric did not take Mystra's portfolio because she did not die, its essence was "just" shattered and some of its fragments were collected by Shar. Shar's plan was described in Forgotten Realms Campaign Guide (page 50), in The Shadow Weave infobox:
Just as Mystra controlled the Weave, the goddess Shar created and maintained the Shadow Weave as an alternative conduit to magic. Not satisfied with her portion, Shar plotted to seize control of both when Cyric murdered Mystra. She miscalculated. The Weave collapsed so completely that Shar not only failed to gather up its fraying threads, she also lost control over the Shadow Weave.
Moreover, as described here (and references therein) there were some other parts of Mystra's essence around the world, confirming that the goddess did not actually die.
There is a series of tweets by Ed Greenwood that adds more details and may add more support to the above interpretation. It seems that there are several Weave anchors (see also here), both places and living entities, that have the role to be a safe net for the Weave. By Ed's tweets (emphasis mine)
Yes, in the sense that they anchor the Weave, which is Mystra, and is arcane magic. It's what allowed Mystra to come back from death, without the entire world being destroyed in the process. In other words, despite a lot of death, destruction, and chaos, there were wizards in the 1300s DR...and there are still wizards in the 1400s DR.
Per my reading, the existence of these Weave anchors added a further complication to Cyric's chance to take the goddess' portfolio.
After Mystra's assassination, Cyric was imprisoned in the Supreme Throne by Tyr, Lathander and Sune, see page 74 of the 4th edition of FRCG: its influence was hugely reduced, and this imprisonment does not seem to allow the god to take over the portfolio of another dead deity. Furthermore, Cyric is driving more and more insane as its confinement in the Supreme Throne goes on.
\$^1\$ A very intriguing aspect, but there is no reference for this.
\$^2\$ From the website: Living Forgotten Realms (LFR) was the flagship Dungeons & Dragons Organized Play campaign for 4th Edition D&D, officially sanctioned by Wizards of the Coast.