Things to test:
1. Item+ Weapon and crits (record 100 grenades with and without), and fraction of ATK (Range).
30 or so Rockets on Koohii (100% damage) -> 7 criticals so probably 8-10% critical; range of damage from 1654-3278 so 1-2x ATK (arithmetic mean of non-criticals and [total critical damage/2] was 1.506456). ATK=1642 (Balanced weapon)
With Item+ Weapon, about the same criticals (9-10%) and the range was 2125-4188 with ATK=1411. This equates to 1.5-3x ATK with arithmetic mean around 2.30.
Item+ did not affect Burst speed (i.e., still takes 2 segments or 50% of action bar).
2. Item+ Weapon does affects Elixirs and Tonics
3. Guard+ weapon: this does damage on all effects (Definitely for physical and magic including group and for Burst, Status, "special" like Judgement)
4. Attack Up (ATK UP) on Item+ Weapon and Bursts seems to increase the variance, seemed to go from 2.1-4.2 (was seeing some 5800 damage on the high end and 3000/2900 on the low end)
5. Dice and effect on criticals: Dice seemed to decrease my chances of criticals on Koohii (only 2)