What is the watch? Android Wear compatible?
Which AquaMail version? 1.5.1 has special stuff for Android Wear - get it here on the forum if you're not seeing the update in Play yet.
If it's not Android Wear, then the notifications are mirrored from the main device (phone), and it's the watch manufacturer's software doing it.
In any case, the default logic for notifications in Aqua is "about all unread messages, old and new". You can change it to "just truly new unread messages" in app settings -> message notifications.