How much item level we need for the new content?

[Astrus]

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Highest casual weapon is 300, and the weapon does impact your damage probably the most significantly. This is one of the more surprising changes from Heavensward to Stormblood that they have made, removing weapons from the level cap dungeons.
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Let's not forget the upgraded weapon for Centurio Seals at 340 (I think just doing the weekly B rank for SB and HW gets you enough seals to buy and upgrade the weapon) and the HoH weapon at 365. While not exactly optimal they can be gotten rather casually and are a step above the 300 weapons. In the case of HoH I can't recommend farming just for the weapon but doing it while you're leveling a class in there is a nice bonus.