I can't get my character's mouth to work right

So this is the first model I’ve ever made and I’m currently trying to fix bone weights and rigging. I couldn’t find a single tutorial on how to make mouths, so i honestly don’t know if I’m doing it right. Anyhow I was trying to get the bottom lip to move with the jaw but it doesn’t look right and I’ve done everything I can think of to fix it.
Here’s how it’s set up: There’s one bone for the jaw. There’s three bones in a line for each lip. The two outer lip bones are connected to the center lip bone. The entire bottom lip is connected to the jaw.