H2H: Shijin Spiral Five-Hit WS, Additional Effect: Plague. TP mods chance of Plague.
Dagger: Exenterator Four-Hit WS, Additional Effect: Accuracy Down. Duration of effect varies with TP.
Sword: Requiescat Five-Hit WS, Non-elemental damage. TP mods Attack (Not sure what it means by this)
Great Sword: Resolution Five-Hit WS, Damage varies with TP.
Axe: Ruinator Four-Hit WS, Accuracy varies with TP.
Great Axe: Upheaval Four-Hit WS, Damage varies with TP.
Scythe: Entropy Four-Hit WS, restores MP based on damage dealt. Damage varies with TP.
Polearm: Stardiver Four-Hit WS, lowers enemy critical hit evasion. Damage varies with TP.
Katana: Blade: Shun Five-Hit WS. TP mods Attack (Same characters as sword)
Great Katana: Tachi: Shoha Two-Hit WS. Damage varies with TP.
Club: Realmrazer Seven-Hit WS. Accuracy varies with TP.
Staff: Shattersoul Four-Hit WS. Lowers enemy magic defense. Chance of effect varies with TP.
Bow: Apex Arrow Triple Damage that ignores defense. Amount ignored varies with TP.
Marksmanship: Last Stand 1-2 Hits, based on ammo remaining. Damage varies with TP.

Assuming this is accurate (and it sounds very accurate to me), the damage of the new weaponskills will pretty much depend on their respective modifiers. Which makes sense, given that modifiers are apparently the bit additional merits will affect.