After the werewolves fought with the Cullens against the army of newborn vampires in Eclipse, and Carlisle attended to Jacob's wounds, Billy Black has changed his perspective on the Cullens. Instead of seeing them as century-long enemies of the werewolves, he now regards them as allies.
Although Billy is not a man of many words, he loves Jacob very much and it pains him to see his son suffer from his problematic relationship with Bella. When Bella returns, he senses that Jacob will confront the Cullens and might put himself in danger, so he tries to stop him, but it doesn't work.
For more info on Billy and his long heritage in the line of Quileute chiefs, check out his "Character Analysis" in our guide to Eclipse.