"Exactly," said Dumbledore, looking very seriously over the top of his half-moon glasses. "It would be enough to turn any boy's head. Famous before he can walk and talk! Famous for something he won't even remember! Can’t you see how much better off he'll be, growing up away from all that until he's ready to take it?" (Harry Potter and the Sorcerer's Stone)
Does the participial phrase take an adverbial role implying the cause of him being better off, or adjective role modifying ‘he’?