Jasper is really not invested in the search for Mr. Hyde at all—as Rachel says, he can do whatever he wants, and right now he just wants to hang out with Rachel and eat a bunch of chicken. He is helping by keeping her company and maybe carrying things? He's good at carrying things. He likes to feel useful, and if he has some task to do, he doesn't have to worry about scary things, like conversation, and the awkward pauses in the middle of conversation.