After 7 playthroughs and 300ish hours, I tried every (default) weapon, here are my boring conclusions
Short answer: they're all viable.
My mainstays are the Acidic Crystal Spear, Black Steel Cutter, and Electric Coil Stick, with honorable mention to the Blind Man's Double-Sided Spear, Acidic Great Curved Sword and Booster Glaive.
The three starting weapons are solid--if boring--choices as they are, but I think their blades are better served on other handles. Bramble Curved Sword or Dancer's Sword are much more fun options as unaltered weapons.
There are too many handles with block or parry as their fable ability. This really hinders the weapons that already have boring movesets and basically begs the player to combine them with something else, and maybe that was intentional
A lot of the boss weapons feel too gimmicky to use regularly, and you REALLY have to rely on fable arts for them to be viable. I love seeing people punish bosses with the Twin Dragon Sword, but I'm not willing to invest all that time into learning how to use it properly.
After ignoring daggers on my initial playthrough, I really gained an appreciation for them because of how often they crit and how fast they are. They can melt mobs and unique enemies alike. The Tyrant Murderer has a fable art that gives it even MORE crits so that's cool.
On the other hand I am NOT a fan of heavy weapons like the Live Puppet Axe. I know people swear by it, but it's slow, clunky, and obscures way too much of the screen. The tradeoff never feels good with my playstyle. As far as axes, I love the way the Carcass Crystal axe feels.
Also, Azure Dragon is very cool. I'm really happy with the cross promotion material and it wasn't just a lazy shoehorned promo