A weapon that is either impossible, unlikely, or impractical in Real Life, but in fiction is both existent and effective, Rule of Cool be thanked.
Usually made of a bunch of cool weapons and mash them together, such as many examples of Mix-and-Match Weapon, or cranking up the weapon's abilities.
Naturally, this often relies on Artistic License – Physics.
The difference with Improbable Weapon User is that these are based on actual weapons, not non-weapon things used as weapons. A Flaming Sword would count as an impossibly cool weapon. A cardboard tube would count as an improbable weapon.
A Sub-Trope of Rule of Cool.
A Super-Trope to:
Absurdly Sharp Blade
BFG (most examples of it, so let's save space by leaving them there)
BFS
Flaming Sword
Freeze Ray
Fuuma Shuriken
Instant Chucks
Laser Blade
Lightning Gun
Macross Missile Massacre (in that a weapon fires more missiles than it should be able to hold)
Mix-and-Match Weapon (many Real Life examples are perfectly practical and reasonable, but fiction often dives headfirst into Rule of Cool)
More Dakka (any weapon capable of it)
Morph Weapon
Precision-Guided Boomerang
Ray Gun (especially before the invention of the laser)
Rocket-Powered Weapon
Swiss-Army Weapon
This Is a Drill
Whip Sword
A Sister Trope of Abnormal Ammo, Cool Sword, Exotic Weapon Supremacy, Improbable Weapon User, and Oddly Shaped Sword.
Compare Cool Starship, Impossibly Cool Clothes, Scary Impractical Armor, Awesome, but Impractical, Weaponized Landmark, and Things Are More Effective in Hollywood.
Compare/Contrast The Power of Index specifically the "(Weapon Name) Are Better" tropes (when normal weapons are impossibly cool by themselves).
Not to be confused with weapons that should overheat but don't.