Previous threads on this:
New Weapon types (included an SE rep response... but they're not thinking creatively to get around the limitations they imagine exist.
and
New weapon classes (same idea)
My thoughts, not to be lost in the threads...
My list of anticipated potential weapon types would be:
#1 want (I'd be really happy if we only got this one added): Dual-ended Sword-Blade polearms
Dual-Glaives (Manes, Double Swords/Spears, Double Voulges, Swallows, "Thief Swords", Bisento, Zanbato, Guisearme) could all be a new variation on Polearm, even sharing the same weaponskills and combat animations.
The heavy spear-like versions would mainly be for Dragoon and the dual-broadsword versions would fit Samurai, but the light Swallow blades (Thief Swords) would be for Thieves, like Zidane. (this would mean adding Polearm skill to Thief, but only given access to Swallows)
Dice: (Setzer) For a unique thrown weapon Corsairs can use. (Certainly not a new skill category, just a variation)
Whips: (Rydia) Ranged weapon, lots of added effects for Beastmaster, Summoner, Dancer
Even without adding new "weapon types", some of those would still be possible without much extra work, making use of existing weapon types. (the main objection to adding new weapons: invalid)
Whips can be added as a "Ranged weapon" and would not need a "new" animation (at most, maybe some special particle effects for elemental whips or something.) They could appear coiled in the hand like Chakrams, and have an invisible strike.
Whips would clearly be equippable by Bst, Smn, Dnc