I noticed last night that my texts didn't pop up on my watch every time they came through. Some did, but I had a lot of texts on my phone in my purse that never popped up on my watch. Is there a setting or something that affects that?
It prioritizes whatever device you have used most recently. So if the iPhone has been or is unlocked, messages will show up there first. If they are not acted upon there, the message should show up on your watch a few seconds later. If the phone is locked, it should come to your watch only.
They won't show up on your watch when you're actively using your iPhone because that's quite redundant and would be highly annoying.
You should get in the habit of hitting the sleep/wake button whenever you're done using your iPhone (it's also a battery saver). If you put it in your purse while still awake, you won't get the texts on your watch and will miss them.