Unfortunately, the Animate Objects spell doesn't have any specific rules in place for using a weapon you already own. Instead, it specifically replaces the damage done by the weapon with damage based purely on size category, and in most cases, magical weapons would not have their effect, RAW. If you want to fight an enemy using flying swords, your best option is the Spiritual Weapon spell in most cases, but only clerics gain access to that spell, and it very specifically summons a weapon into being. Neither of these are ideal for your telekinetic army of swords.
Acyrra's Animated Weapon is a spell which exists to fill that niche; it is similar to Spiritual Weapon in a few ways, but it differs in many others; the main thee differences are: the requirement to animate existing weapons rather than summoning them, the requirement of concentration, and the ability to animate more weapons at higher levels rather than dealing more flat damage.. It exists to allow Bards, Wizards and Sorcerers to take on the aspect of Scaramouche, or Darth Traya, fighting off enemies with magically animated weapons.
Rules Clarifications: Concentration: You must make a concentration saving throw as if you were hit by an attack whenever one of your animated weapons is struck - however, failing that save only loses you control over the weapon that was hit. An enemy will have to attack you personally if they wish to break your concentration and disable all the weapons at once. Opportunity Attacks: Since these weapons are not creatures, they cannot make opportunity attacks. Optional Flanking Rules & Sneak Attack: These weapons are not creatures, so they cannot flank a creature or grant a Rogue sneak attack. Weapons stuck in another creature: If a weapon is stuck in another creature's body, it is not currently being used by that creature and it is not animate in most cases. If the fighter leaves his greataxe sticking out of another creature's body, or throws a handaxe at a dragon flying through the air, you have a perfect opportunity to use this spell. Weapons in a creature's inventory: This would largely depend on where the other creature is storing their weapons. If they have a weapon or two stuffed inside of a bag, you can't exactly see it, but otherwise, you could animate your Rogue ally's daggers that they're not using. The spell does not require the items to be unattended, just not in use, so get creative. Improvised Weapons and Arrows: While I would personally allow a PC to use this spell on arrows sticking out of a creature's body specifically, arrows are improvised weapons, and are not melee weapons RAW. Likewise, other improvised weapons such as a table leg cannot be affected by this spell. The only objects which can be affected are melee weapons.
Ideas: Using this spell to its potential becomes more and more difficult as you increase the spell level, since it does not summon weapons into existence, but requires them to already exist somewhere on the battlefield. While at early levels it's very doable to throw a handaxe at a creature and then cast this spell, at later levels it may take more strategy to have access to a variety of powerful weapons to animate across the battlefield. However, a well-equipped party always have a variety of options available; You could animate weapons on your allies' person(s), or animate the weapons of fallen enemies. It may also be useful to ask the DM if the enemy assassin has a dagger attached to his belt. You could also always carry around a number of weapons on your person for use with this spell, though your ability to control the battlefield using this spell will be limited in doing so. As the weapons can only move 20 feet per turn, having a variety of different weapons located at different spots across the battlefield is the most ideal way to use this spell, so you can cover more ground and keep enemies from simply walking away.
So, thoughts? Ideas? Revisions? Rules questions? Please send them at me, this is a fairly complicated spell so it's hard to get the balance just so.
Unfortunately, the Animate Objects spell doesn't have any specific rules in place for using a weapon you already own. Instead, it specifically replaces the damage done by the weapon with damage based purely on size category, and in most cases, magical weapons would not have their effect, RAW. If you want to fight an enemy using flying swords, your best option is the Spiritual Weapon spell in most cases, but only clerics gain access to that spell, and it very specifically summons a weapon into being. Neither of these are ideal for your telekinetic army of swords.
Acyrra's Animated Weapon is a spell which exists to fill that niche; it is similar to Spiritual Weapon in a few ways, but it differs in many others; the main thee differences are: the requirement to animate existing weapons rather than summoning them, the requirement of concentration, and the ability to animate more weapons at higher levels rather than dealing more flat damage.. It exists to allow Bards, Wizards and Sorcerers to take on the aspect of Scaramouche, or Darth Traya, fighting off enemies with magically animated weapons.

Rules Clarifications:
Concentration: You must make a concentration saving throw as if you were hit by an attack whenever one of your animated weapons is struck - however, failing that save only loses you control over the weapon that was hit. An enemy will have to attack you personally if they wish to break your concentration and disable all the weapons at once.
Opportunity Attacks: Since these weapons are not creatures, they cannot make opportunity attacks.
Optional Flanking Rules & Sneak Attack: These weapons are not creatures, so they cannot flank a creature or grant a Rogue sneak attack.
Weapons stuck in another creature: If a weapon is stuck in another creature's body, it is not currently being used by that creature and it is not animate in most cases. If the fighter leaves his greataxe sticking out of another creature's body, or throws a handaxe at a dragon flying through the air, you have a perfect opportunity to use this spell.
Weapons in a creature's inventory: This would largely depend on where the other creature is storing their weapons. If they have a weapon or two stuffed inside of a bag, you can't exactly see it, but otherwise, you could animate your Rogue ally's daggers that they're not using. The spell does not require the items to be unattended, just not in use, so get creative.
Improvised Weapons and Arrows: While I would personally allow a PC to use this spell on arrows sticking out of a creature's body specifically, arrows are improvised weapons, and are not melee weapons RAW. Likewise, other improvised weapons such as a table leg cannot be affected by this spell. The only objects which can be affected are melee weapons.
Ideas:
Using this spell to its potential becomes more and more difficult as you increase the spell level, since it does not summon weapons into existence, but requires them to already exist somewhere on the battlefield. While at early levels it's very doable to throw a handaxe at a creature and then cast this spell, at later levels it may take more strategy to have access to a variety of powerful weapons to animate across the battlefield.
However, a well-equipped party always have a variety of options available; You could animate weapons on your allies' person(s), or animate the weapons of fallen enemies. It may also be useful to ask the DM if the enemy assassin has a dagger attached to his belt. You could also always carry around a number of weapons on your person for use with this spell, though your ability to control the battlefield using this spell will be limited in doing so.
As the weapons can only move 20 feet per turn, having a variety of different weapons located at different spots across the battlefield is the most ideal way to use this spell, so you can cover more ground and keep enemies from simply walking away.
So, thoughts? Ideas? Revisions? Rules questions? Please send them at me, this is a fairly complicated spell so it's hard to get the balance just so.