2k stays in battle.
I've seen this debated (recently, too), regarding what really happens to weapons during and after battle. I'm actually leaning to the other side of this ruling, due to the following from
the REG:
Weapon-Class Enhancement
This is a special kind of enhancement marked by a shield icon on the left side of the card. Weapon-class enhancements may be held by warrior-class characters outside of battle, and may be placed on a warrior-class character during a player’s preparation or discard phases. The special ability on a weapon-class enhancement only activates in battle. Weapons follow the same rules as placed cards by following their bearers to any location in which they are moved. Weapon-class enhancements can also be played during battle using the rules of initiative.
Following battle resolution, when enhancements are normally discarded, a warrior-class character’s controller may decide to keep one weapon-class enhancement on the warrior-class character.
Based on the wording of the rules, I would rule that if a weapon has been placed on a character in a previous phase (previous battle or during a prep or discard phase), then that card is now "placed" on the character. They are treated as placed cards from that moment forward, by all other rules and abilities (see Capture and Convert for similar examples, where they state what to do with the weapons on the character). It is not just limited to outside of battle, the rules seem to indicate a state where that weapon is now placed on that character, if it was done during a prep/discard phase or if it was kept by the holder after a battle in which it was played.
My ruling would be that Tartan could take 2k Horses only if it were played
from hand during the battle, and was not previously held by Assyrian Siege Army. If it were previously held, prior to entering battle, then it would be removed from game with ASA.
Note that I know some people will disagree with this assessment, but that is how I read the rules on it.