Character editing could be considered either "big picture" editing or "little picture" editing, depending on what aspect of the character(s) you're editing.
First is the question "Does this character work?" For my first expanded draft of A Fistful of Fire, the answer was "No." Evonalé was downright whiny, as one friend told me when she couldn't get through the first section.
That whining happened because I had too much paranoia in there, too much of one feature. It's like having a nature trail that's in a forest, but 90% of the trees are all oaks. Some folks will still enjoy it just because they like trees, but people tend to prefer some variety in what they see.
And then there's the question "Does this line work?" This question comes in when you're giving the characters individual voices, their own preferred words, their own vocal quirks*—and when you're making sure that the character's coming across the way you intended.
I had to ask that question in every paragraph and line of every scene as I edited A Fistful of Fire so Evonalé wouldn't be unbearably whiny. But even that is a little-picture application of a big-picture edit.
Writing Destiny's Kiss put me face-to-face with the "little picture" form of "Does this line work?":
With what's already in the scene, does this line go overboard?
Destiny's Kiss features a vampire, Ambrogino Romazzo, who's… an unusual blend of traits, in part because he's had to raise his little sister, who's the narrator's age. The narrator has to figure out if he's a nice guy or a creep, and one little line garnered beta comments that it went too far in the wrong direction.
Granted, I've also received "Ick!" comments on the pair of first cousins who are also a couple in "The Corpse Cat". Folks' "too much" meters differ from each other, but too much of anything will wreck your character.
Nice contradiction there, no?
All you can do is make sure the features balance out and don't all congregate in a particular section. Vary up the oak trees with maple and apple and shrubbery—and intersperse them appropriately, so the reader doesn't get distracted by a sudden willow when no creek's been built to water it.
Having a trusted first reader of a different upbringing than you can help find these sorts of problems—because folks with your same upbringing will probably make the same assumptions you do, understand things the same way, so they won't catch when you leave out character motivations and such—they'll understand what you meant.
At least, folks with similar upbringing to you will be more likely to understand what you meant.
Have you ever read something where a single aspect or line made the character not work? What about written something where something made the character come across differently than how you wanted? Who caught it?
*For an example with fantastic individual voices for the characters, I recommend Chime by Franny Billingsley.