Field Control - Who places weakened?

[Cathayan]

For the Targaryen card Field Control when the opponent places on the horses does he determine which unit gets the weakened token or does the player who played the card?

 

[Yelraek]

The player who owns the effect controls the effect.

Opponent claims horses. Targ plays card to change the effect of horses to make a unit weakened (along with another effect). The opponent who claimed horses now continues to use the effect from claiming the horses (which is now the Field Control effect).

And if I may predict your follow up. Yes, that player may choose to apply the effect to an already weakened unit.