I dont think 3 was a good movie, though I do marvel at its script. It's a really interesting story about the colony. I have no idea how it was sold as a good idea for a film in the Alien franchise.
Yeah it's basically straight up an Rogue Trader-era era Warhammer 40K story, to the point where if it wasn't for the long history of the scripts for Aliens 3 and the large amount we know about them, you might think that was inspiration (40K WAS the inspiration for Event Horizon, note, as confirmed by the director a while back).
The Kingsman: The Golden Circle
The Kingsman was a fun movie. Not a masterpiece, but besides a very weirdly placed joke near the end I can't think of anything I would change. The sequel, on the other hand, is the type of movie that gets worse the more you think about it.
This is a strong contender. We go from a genuinely fun movie to a truly offensively stupid one which reveals the director did not, in fact, understand his material, and just got lucky.
Personally my one would be
The Dark Knight Rises.
The Dark Knight was a very good Batman movie, a pretty good movie period, featured great performances, a memorable script, and a plot that, for a superhero movie, was surprisingly plausible on its own merits (Joker's plan falls apart under examination, but the film is good at avoiding that - it's not blatant). It's also quite together and focused.
The Dark Knight Rises is an risible wet fart of a movie, which looks good, and has some nice action sequences, but is absolutely brain-damagingly stupid, filled with highly politicised and very odd ideas (which lean very hard in a specific direction which isn't really congruous with even some of the movie's other ideas), blatantly makes no sense on many levels, has a largely terrible script with clunky lines (only Bane gets much to say, and he started off Nolan's godawful trend of "it's fine if the audience can't hear/understand"), is wildly overstuffed with characters and ideas - and not even in a fun way, and is overlong and self-indulgent on top of all that.
It went from like a 9/10 (grading on an curve for action-y movies) to like a 4/10.
Re: whether we're talking about "worst sequel" or "worst movie that is a sequel", I feel like the quality of the previous movie must be considered. Otherwise we just trawl around the trash for a trash sequel to a trash movie. I don't think it's interesting to ask what is the worst movie that happens to be sequel. It is interesting to ask what movie is the worst sequel to the previous movie. I don't think it's just quality either - some sequels completely betray the themes and ideas of the original - Starship Troopers 2 has been mentioned, for example. Robocop 3 is a truly terrible movie and completely betrays all the ideas of Robocop (Robocop 2 is bad but doesn't do that). Die Hard 2 is a pretty good movie, but McClaine is kind of a Big Damn Hero in it which is very distinct from the guy who was barely surviving in Die Hard.