Around the bronze age, when Gwen Stacy died. That's when comics started getting more serious overall, but still didn't take themselves too seriously.
Then Watchmen, Dark Knight, et al, came along. Good comics in their own rights, but they influenced everything else in a bad way. Now everyone wants their brightly-coloured superheroes to be super-duper serious dramas about the nature of humanity.
Mind you, comics can be that, but I find it contradictory to have most superhero comics try to be serious when it's kind of silly to see people dress in bright circus suits and fight equally brightly-dressed supervillains.
I think that's one of the reasons why the MCU is so successful. It tries to be just serious enough so you care, but it doesn't pretend it's a hardcore drama about the human condition.