Any of the weapons in Final Fantasy II Advance can be used by all characters. The initial weapon of the character is usually their strongest weapon. You need to equip a weapon, and continuously use it in battle. When this happens, your proficiency with that particular weapon goes up. It is a good idea to have two major fighters with swords/axes, and have your back defense use bows, to give them the full damage ability.
In the Soul of Rebirth, you will get three new weapons, for your three weapon users. Scott will get a sword, Minwu a Staff, and Ricard will get a lance.

Swords
NAME	COST	NOTES
Blood Sword	-	Transfers damage as hp
Broadsword	400	-
Long Sword	600	-
Mythril Sword	1800	-
Ancient Sword	-	Causes Curse
Sleep Blade	-	Causes sleep
Wing Sword	5000	-
Gaia Blade	-	-
Flame Sword	-	Deals Fire damage
Defender	-	Raises evasion
Ice Brand	-	Deals Ice damage
Sun Blade	-	damage vs undead is doubled
Excalibur	-	-
Masamune	-	-
Wild Rose	-	(Only Scott can use)

Knives
NAME	COST	NOTES
Knife	150	-
Dagger	400	-
Mythril Knife	800	-
Main Gauche	-	Increases evasion
Orichalcum	-	-
Ripper	-	Knife with razor sharp edge
Cat Claws	-	-

Axes
NAME	COST	NOTES
Axe	500	-
Battle Axe	800	-
Mythril Axe	2000
Demon Axe	10000	-
Ogrekiller	15000	Extra damage vs ogres and giants
Poison Axe	-	May cause Poison status
Rune Axe	-	Effective vs magic foes/casts Fog6 as an item

Bows
NAME	COST	NOTES
Bow	150	-
Long Bow	250	-
Mythril Bow	1000	-
Dark Bow	-	May cuase blindness
Flame Bow	-	Causes fire damage
Ice Bow	-	Causes ice damage
Yoichi's Bow	-	Casts Berserk3 as an item

Spear
NAME	COST	NOTES
Javelin	300	-
Spear	500	-
Mythril Spear	1500	-
Trident	5000	-
Demon Spear	10000	-
Flame Lance	15000	Causes fire damage
Ice Lance	-	Causes ice damage
Thunder Spear	-	Causes lightning damage/casts Bolt16 as an item
Holy Lance	-	Causes holy damage/casts Holy8 as an item
Wyvern Lance	-	(Only Ricard can use)

Staves
NAME	COST	NOTES
Staff	250	-
Mace	500	-
Mythril Mace	1500	-
Werebuster	3000	Double damage vs Werebeasts
Mage's Staff	-	Casts Bolt5 as an item
Power Staff	8000	-
Wizard's Staff	-	Casts Venom16 at a random target as an item
Healing Staff	-	Heals target when strikes
Diamond Mace	-	-
Stardust Rod	-	(Only Minwu can use)