You "improved" SWGriff from 4 to 5? And waited 336 hours? Man...
For weapons you're not clear how those got there - has someone else access to your PC?
For not earning XP on different weapons in the game... II confirm it. Ingame XP improvement will not work any more after you "cook" at least one weapon here:
http://heroes-6-conflux.uk.ubi.com/soulforge
And an idiot - me - just did the cooking to check it up and now I'm scr...d!

So a warning - do not test this unless you're prepared to wait 336 hours for leveling a weapon from level 4 to 5!
And no, cloud sync has no impact on this issue, I've tried with sync turned on and off.