Can someone explain weapon stats?

[Gokuhan]

So even though the secondary stats are still Crit>DET>SkS for DRG loosing weapon damage (and by extension STR) is actually Cheating me worse.

That's it exactly, weapon damage trumps all. As far as Skill Speed is concerned, it's main purpose has always been to lower the OCD, however it's usefulness has always been up in the air and it can cause people to easily run out of TP during long fights, so in a recent patch it was changed to also give a slight boost DoT damage.