Will always get some differing opinions on this, but for a rundown of all the weapons (though ignore the Orifalcon weapons, they're Scenario 3 only), see http://www.celestialdamnation.com/jumes ... apons.html
It also depends on which type of weapon you have them all trained up with. I, like many others, will train all characters with all weapons, so I have plenty of choice
Anyway, what I'd usually have equipped on whom, and why:
Medion - Final Rapier: Agility +5, Critical +5, Regains 2MP a turn, and special 'Das Ende' is obliterator-type. God Rapier is a good second - I like the spell 'Thanatos'
Campbell - Ultra Lance: Highest attack, magic boost, and gives obliteration-type special. Dragon Lance comes in as a close second, as it has the same attack as the Ultra Lance, but is also good against Beasts. Lack of magic boost drops it some points.
Syntesis - Tiamat Rod: It's the Tiamat Rod. Who doesn't love that spell? Having Defence +5, Movement +1, and Luck +2 is also a bonus.
Uryudo - Mitra Ankh: My Uryudo is usually a super beast by the end of the game, so having Thanatos as an attacking spell is great. The Dark and Light resist also come in very handy.
Waltz - Breaker Bow: Defence + 7, excellent special, strong against demons, and greatest attack boost. 'nuff said.
Rock - Gaia Axe: Defence +2, Agility +5, Regains 2HP a turn, gives special Giga Wheel, and can use to cast Aura Lv1 (if you need to). Rock's low HP is greatly assisted by the regaining 2 HP per turn.
Bernard - Same as Waltz: Breaker Bow.
Zero - Shiva Sword/Levantine Sword: Both give same attack, but different bonus' of +30 (light for Shiva, Fire for Levantine). Whichever you think is best for the final battles.
Hazuki - Rumbling Sea Katana: Strongest Katana you can make. Other's are less attack power, and the one you find is cursed. Hazuki does better being able to change to Shuriken's when you want a long range attack
David - Sky Thomahawk - 1-3 range is brilliant. David's just not that great a character.
Hedva - Earth Wand: Thor spell is the most powerful spell in the game. Lightening resist of +40 is good.
Hera - Jewel Glove: Two attack points less than the Magna Glove, but Hera's a bit slow, so the plus 5 agility goes a long way. Gives Counter +4 and Critical +5 as well.
Robbie - Storm Shot: Agility +3 is best thing about it. Weakest power upgrade of the three Shell bows, but Robbie has decent enough attack that dropping 2 points isn't that bad.
Arthur - Rune Spear: Magic bonus this weapon gives is great for the magic Knight, and a plus 25 lights resist is a great bonus.
Jade - Storm Shot: Same as Robbie. Not bad attack for a character, and requires more agility.
Penko - Silver Beak: only Mithril beak you can get made. Choice made for you.
Pappets - Queen Whip: Best attack boost.