What are the best weapons?

I'm a bit confused by the question, so I'm gonna answer as best as I can.

Best weapon based on ability - Can't really answer due to dependence on situation.

Best weapon based on user's animation - Either Thögn's and L!Lucina, or Swift Mulagir and L!Lyn.

The Exalted Falchion of Archanea is pretty friggin good. Larths Fire Emblem special just combines so we'll with it, giving him buffs on top of buffs. Combine that with Spd/Def Bond, and he is almost indestructible. Plus Larths classic and badass quadruple stab is just pure eye candy.

(Totally not bias to Larth)

Ability: Any Armads, any Falchion, Thani, Forseti, Hlioskjalf (B!Veronica's staff), Royal Sword, etc.

Animation: Forseti, Odin's Grimoire, Missiletainn, Mjolnir, Thani, etc.

User-based (if you meant how well they sync with the user): Any Armads, any Falchion, Forseti, Garm, Vassal's Blade, Thogn, Hoarfrost, etc.

Just to name a few.

Flame Siegmund on L!Ephraim is one i love. It fits with his movement type, it fits with his high atk, and the animation is cool. It’s kinda bad on regular Ephraim tho due to Infantry movement

Expiration
Loptous
Divine Naga
Keen Gronnwolf

Based on effects.....
Wepons that has cooldown reduction effects (summers breath, maltet, wing sword+)

effective against armors/horses/dragons (thani, dauntless lance, binding blade+)

Increases number of attacks (armads, dire thunder, hoarfrost knife)

Decreases enemy attacks (thunder armads, great flame,deathly dagger+)

Lets you deal true dmg ( berserk armads, nameless blade+, giga excalibur)

Has built in DC (.....)

Or has a really unique effect and/or can support the team (forsetti, felicias plate, valflame, winds brand+)

Tough question but I think Odin's Grimoire has probably the coolest animation in the game now, and matches Odin perfectly.