Why didn't any of the subsequent films or sequels get weird?

Because the words "Star Trek" and "camp" were stuck together as if they were glued together back during the 1970's by popular culture observers. These observers in the media and the entertainment world had only a very small level of interest in Star Trek so their knowledge was equally minimal. If they only saw a couple of outlandish episodes then they just assumed the rest of the series was the same way. Because these observers such as the Saturday Night Live set of comedians appealed to the anti-authority nature of young people they were given the benefit of the doubt as to what they knew on a wide variety of subjects. Benefit that should have never been granted. Ironic that these people criticized establishment types for the "anything for a buck" mentality that was eroding America when these comedians were employing "any zinger for a buck" even if overall it was not a very accurate assessment of a subject. Getting back to the topic at hand the producers of TNG and onward were so afraid of being held up to ridicule that they avoided such subject matter that you brought up that they avoided anything that had a taste of TOS other than the fact the show was a Star Trek derivative so it would have space ships, aliens, exotic weapons, and so forth.

I wish that they had. I feel like the spin-offs, and ESPECIALLY the people behind them, took themselves way too seriously.

Well, the camp style was really big in the 60s and wouldn't have played well in the 80s. If it did, other things like Tim Burton Batman film would have featured Jack Nicholson dancing and surfing with Michael Keaton. Some of the camp stuff in Star Trek and other shows of that era was really kind of a giddiness about being able to shoot TV in color for the first time. A lot of those shows really enjoyed bright colors and goofing around with the cameras. The thrill wore off after a few years.

Star Trek V was plenty weird. Early TNG "went there" occasionally too.

Campy episodes, for me. Not saying they are all bad but in the CAMP style. Shore Leave, Spock's Brain, And the Children Shall Lead, the MUDD episodes, Assignment Earth, Let that be your last battlefield, Plato's Stepchildren, Day of the Dove, Who Mourns for Adonis, Wolf in the Fold, The Omega Glory, Bread and Circuses, The Squire of Gothos and The Apple.

Because later Trek took itself too seriously and didn't know how to have fun.

They did if I recall .... there were quite a few almost slap-stick scenes with the doctor, and then there was the doctor on Enterprise, and Seven of Nine. I never watched Deep Space 9