I'm assuming you've looked in the Watch app and have confirmed your settings are good (like set up "Mirror My iPhone" for Messages)?
I have noticed some weirdness in that most of the time:
- if I'm using my phone, notifications will show up on my phone and won't show up on my Watch
- if my phone is locked, notifications will show up on my watch and not my phone.
All of which makes sense. Except that it's not 100% consistent. Just now, for instance, while using my iPhone to type this response, my watch (rather than my iPhone) just alerted me to a Calendar reminder. So it's a little wonky.