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Please watch this video published by German YouTuber shoot2loot in which he shows that the increased Weapon Damage for Signature Weapons, coming from Grades, gets converted to All Weapons Damage after logging out of the game and back in (with the same character):
">A quick explanation with screenshots:
Exhibit a)
The first screenshot shows the build without any investment into All Weapon Damage (apart from the 10% granted by Keener's watch).
Exhibit b)
The next picture shows that no weapon got upgraded – except for the Specialization weapon, being Grade 14. Thus getting +14% Weapon Damage.
Exhibits c) & d)
The following screenshots show the correct numbers for the All Weapons Damage for the primary AR (+10% from Keener's watch) and the TAC (+10% from Keener's watch + 14% from Grade 14 = +24%).
Exhibit e)
Finally, testing the primary AR deals 105,998 damage with a regular hit (no headshot, no crit):
Exhibits f) & g)
As you will be able to see in the video, the tester will then log out of the game and directly log back into it with the same character. The following two screenshots are taken after this procedure and show the All Weapons Damage for the AR – which now shows 24% instead of the correct 10%, equalling +14% from the TAC's upgrade – and the Specialization weapon – which now also has 14 additional percent.
Exhibit h)
The last screenshot shows that this is not only a display bug, but that also the actual damage inflicted to the target got increased (up to 116,598).
Conclusion
This should be looked into asap as this damage transfer from Specialization weapons to every weapon, caused by logging in and out of the game, is most probably not working as intended.