He changes because of Luke’s unwavering evaluation that there’s still good in him.
In A New Hope, Darth is just the Contagonist. He doesn’t present any perspective that’s challenging to Luke. Obi Wan is challenging Luke to stop trying to measure up and put his trust into the force, which allows him to change. (Crucial Elements: Test / Trust)
In Empire, Darth is trying to tempt Luke to the Dark Side, but this is again an OS issue. Seeing the greatest Jedi warrior is a shriveled, short, weirdo hermit is what allows Luke to abandon trying to be good enough and go save his friends. (Crucial Elements: Accurate / Non-Accurate)
In Empire, you finally have Darth as an IC, but Luke is steadfast. His evaluation that there is still good in his father allows Darth to see it’s not too late and redeem himself. (Crucial Elements: Evaluation / Reevaluation)