Apple watch showing old notifications
This is a watchOS 2 Bug
The issue as described is basically that old, previously read/dismissed messages in a conversation continue to show up when new messages arrive (zombie messages) long after they were initially received and were marked as read.
The fix described here is to delete the offending conversation on Apple Watch. Once this has been done, notifications for conversations with that contact will begin to function normally.
Doing this will not delete the conversation from any other device so you don't have to worry about losing your conversation, so even though it seems destructive, this is a non-destructive fix in that sense.
Note: the next time a notification for that same contact is received by the watch, the deleted conversation will be restored and viewable from the watch. Prior to that the conversation will not be present within the watch's Messages app's conversations list.
Sometimes, you may not know that the configurations of your Apple Watch push notification system is different from your iPhone. The phone may receive the latest messages while the watch is lagging or doesn't receive any at all. This post might help you out.