What movie sequels do you consider to be superior to the original film, and what specifically makes them better?

I somewhat had more fun with Back to the Future Part II than the first movie.

Gonna go out on a limb here and say Guardians of the Galaxy Vol. 2. Yes, I'm a broken record I know. I've been praising this movie since 2017 and it's never stopped blowing my mind (and it still doesn't make sense to me that this is a hot take).

It took what was my favorite movie back then and just expanded on it so much. It's better than the original because it focuses 100% on what made the first movie special: The characters.

We had a deeper look into all of the main characters, got to explore their deeper fears, and how those scars affected their companionship. This is a sequel that understood that the most compelling conflict you can have in a story is the one we each carry within - and ultimately, it's a conflict no one can resolve on their own, but it gets easier to deal with when you're surrounded by people who truly care.

Of course, the movie gets an actual supervillain too, but Ego the character is as much the villain here as actual ego. And by making the villain someone who actually matters to the story of the protagonist, that makes every part of the story compelling - a contrast to the first movie which can really drag whenever the villains are on-screen.

I went into the theater to watch this genuinely stressed about how it'd live up to a film I loved so dearly, and came out of the theater blown away and with a real certainty that this was going to be my favorite trilogy. Because, yeah, after this it was very obvious that James Gunn could do no wrong with these characters.

Terminator 2 is maybe the best example of a good movie that went great in the sequel

My vote goes to The Dark Knight.

These sorts of threads always inevitably boils down to the subjective battling against the objective, with the subjective slaying the objective by a score of something like 99 to 1. But my vote would be for Friday the 13th. I always thought the next three movies were far better than the first one.

The godfather part 2
The lord of the rings the two towers
Terminator 2

Certainly up there but I think the nod goes to Empire. 

Terminator 2

Spiderman 2

Captain America 2

The lord of the Rings: The two towers

Agree on Dark Knight (also Batman Returns), Spider-Man 2 and Captain America 2.
Blade 2 (arguable, but IMO).
Mad Max 2: Road Warrior and Desperado are really better because the original had so small budget but nevertheless.
And of course Empire Strikes Back.