Caladbolg(Ultima Weapon in Japanese Version) - Does more damage when Tidus' HP is full, no effect on Aeons.

Nirvana- Does more damage when Yuna's MP is full, and allows Valefor to exceed 9,999 damage.

World Champion - Does more damage when Wakka's HP is full, and allows Ifrit to exceed 9,999 damage.

PuPu The Ultimate Smurfing Total Pwnage Blue Alien Onion Knight - Does more damage when Lulu's MP is full, and allows Shiva to exceed 9,999 damage.

Spirit Lance(Longinus in Japanese Version)-Does more damage when Kimahri's HP is full, and allows Ixion to exceed 9,999 damage.

Masamune - Does more damage when Auron's HP is depleted, and allows Yojimbo to exceed 9,999 damage.

God Hand- Does more damage when Rikku's HP is full, no effect on Aeons.

If you want a weapon that do constant damage, go get a customized one.