Because Tony is the only one who's been shown with an interest in expensive watches. He was depicted selecting one from several options at least twice previously. Also, Clint is the one who was meant to keep the Avengers grounded, so perhaps he made himself the protector of the remains of the Avengers compound.
I'm going off that precedent. However, I acknowledge it may be that the show
wants me to think it's Tony's watch.
If it isn't, I think it's more likely a relic from Clint's era as Ronin. Even if his wife was a SHIELD agent prior to getting married (and that could explain how they met - perhaps she was based in Germany - and it could also explain Clint's comment about it belonging to someone he used to work with who's been out of the game for a long time), she was never an Avenger, so why would her watch have been kept in the Avengers compound?
If it's a Ronin relic, that could also explain why Maya was after it.
Maybe the watch was Clint's - given to him by Tony - and the tracker was so Laura could keep tabs on him.
Or maybe it was Laura's from when she was an active field agent and Clint kept it in his room at the compound as a memento or something (and/or so the built-in tracker couldn't be used to find his wife and family).
Hopefully they'll explain it by the last episode.