At MegaCon in 2014 (via StarWars.com), Mayhew briefly explained that the maneuver was something that developed as a result of his constantly needing to duck in order to fit through doorways. Some of the doorways and passageways on various “Star Wars” sets are a little small by design, of course, but Mayhew probably had to duck through most doorways, given that he was a gargantuan seven feet, three inches tall. (For some context, former basketball player and entertainment personality Shaquille O’Neal, is seven-foot-one, a full two inches shorter.) When you’re that tall, every doorway is a potential bonk to the head, whether it’s built by the Empire, the Rebellion, or a bunch of furry little dudes on a forest moon.
Maybe Mayhew got so used to tilting his head to one side to get himself safely through doorways that he just instinctively did the tilt during other moments, like whenever he’s listening to Han explain something. It’s also possible that since Mayhew is usually looking at whoever’s talking and they’re guaranteed to be shorter than him he’s trying to get his eyes slightly more on their level without looming over them. Whatever the reason, the result is that Chewbacca feels more truly alive.