Here's one really specific detail I found interesting -- it was a comparison made in Story by Robert McKee that's rung true for me:
The difference between a character who is comedic versus a character who is sympathetic is whether or not they're aware of their own shortcomings.
The characters that we're meant to laugh at are the characters who don't know or think that they're doing anything weird or wrong. The wacky sidekick who just won't leave the hero alone is funny when he seems oblivious to how obnoxious he is, and we laugh when the hero says ".....oh no," when the sidekick shows up. But take that exact same character dynamic and make the wacky sidekick aware of his flaws -- he knows he came on too strong, he knows when he's messed up, he knows the hero's frustrated with him but he's trying to do better -- and suddenly we side with the sidekick, and we don't laugh as much at the hero's exasperation -- in fact, the hero seems like a big jerk, now.
I've used this a LOT in my writing; introduce a character who tries to play off his problems and pretend they aren't there, and you have a character who's really easy to not take seriously. Reveal that the character is genuinely frustrated, afraid, or upset about their own flaws, and suddenly they become much more sympathetic.