There’s a moment in the Last Jedi when Chewie breaks down Luke’s door. Luke starts to say something, then pauses. “Wait, where’s Han?”
It’s a moment with a lot of weight; Luke seeing Chewie and recognising that Han should’ve been there, too. In fact, it’s why Chewie was there.
Rey had already proven that she could fly the Falcon well and by herself. In fact her first command of the Falcon is the last high point in the ship’s history. Even Lando doesn’t get to do anything cool with it.
But to the point, Rey didn’t need Chewie to come along, and if her plan to be trained by Luke held, then Chewie would have a long wait on the planet.
So why’d he come? Because when your best friend dies, you should be the bearer of the bad news, not someone Luke’s never met before.
There’s the added layer that Chewie was Ben’s godfather, Luke was Ben’s trainer, and Ben killed his own father. Chewie had the opportunity to kill Ben, right then and there, but couldn’t do it. That too is something he’d want to tell Luke.
That little moment of realisation on Luke’s part is one of the great pay-offs of this universe. However, there are no ramifications of it, which seems to cheapen the moment.
But what of Chewie? Basically he’s done the last act he needs to for Han. He’s a free agent, his life debt paid off. Of course he chooses to stay in the fight and not just return to Kashyyyk. He cares about Princess Leia and Luke. He may even care about the struggle, having seen the empire’s impact on his homeworld.
But is Chewie changed by Han’s death?
I’d like to think that Chewie is a bit more of a risk-taker after Han dies. We have the impression that Chewie checked Han’s crazier impulses, but I think the opposite was also true, that Chewie sometimes gave in to his impulses, and Han (or Leia) reeled him in.
Think of Chewie growling at Vader or strangling Lando on the cloud city.
Without Han, Chewie got less risk-adverse, and he got caught by the First Order for it. And as an aside, his apparent death should have been his actual death. It’s not like they did anything else with his character after that moment.
Chewie was often an under-utilized character, but that doesn’t mean he didn’t have feelings or never changed.