What is fat? It very much depends on where you are. Scientifically speaking, I'm obese. At home, in Barbados, I'm thick, which is a good thing. In the US, I'm fat. And in Japan, I'm Godzilla. Where is your character located? Is she fatter than the average person there?
Black girls tend to be a little bit bigger than white girls. Asians can acheive a miniscule-ness undreamed of by the rest of us. Is your character big for her race? Or just big in general? Is she the only black girl in a school full of Asians? Is your character used to being fine by Western ideals, but when she moves to Japan finds herself suddenly humongous? (ORCHARDS)
Reality vs. Perception
Is your character actually fat, or is she just convinced she is? (The DUFF)
How does your character feel about her size? Does it hold her back in everything? Does she go out and conquer the world anyhow? (WILL GRAYSON, WILL GRAYSON) Is she perfectly happy with her size? (THIS BOOK ISN'T FAT IT'S FABULOUS.)
Clothes can be the bane of a fat person's life. Nothing fits right. Lots of fat people hate shopping because you always have to dig around and find the 5 styles that are available in your size. That is, if you can even shop in a regular store.
How big is your character? Decide her exact weight and height. If you're not modelling her off someone you know, find a picture online or in a magazine if you can of her size and shape. Does she need to shop in specialty stores? What's her relationship with clothes? Does she wear whatever, because nothing looks good? Is she always deluding herself and stuffing herself into clothes that are a little (or a lot) too small? Has she given up on her frame in favour of accentuating something else? Eyes, hair, feet? (IN HER SHOES) Is she a fashionista who knows exactly what colours and styles to wear to be the sexiest she can be?
Sophie's got style. (ANASTASIA)
In women's fiction, and in extreme cases in YA and MG fiction, the character's size might cause health problems. These can range from smaller issues like sore feet and being out of breath after climbing two flights of stairs. Or they can be more serious. Like having diabetes, or being at risk for it, etc.
Boys to Men
How does your character's size affect her relationship with guys? Do men overlook her? Is she one of the boys? Do guys go for her crazy confidence? Does she love 'em and leave 'em? Is she afraid to have sex because it involves baring all? If she's an adult, how have the years of her relationships with guys affected her?
Every day life
When your character gets past a certain size, that trickles into every day life. Maybe she can't fit in airplane seat/seatbelt. Maybe she prefers to stand in buses because some of her will trickle into the neighbouring seats. Maybe she doesn't go with her friends to the beach, because she'll have to wear a swimwuit. And she doesn't hang when they're being active, because she's afraid her fitness level will embarrass her.
Universal things may also embarrass her. Like if there's a squeaky chair, a skinny chick sits in it, and thinks, "ha! the chair made a funny noise!" Our fat chick sits in it and thinks, "Oh my God, I'm so fat now that even the chairs are protesting." Some fat chicks take care about how much they're seen eating in public. They may develop issues with skinny friends who can eat everything.
What it doesn't affect
Unless your fat chick is so tangled up about her weight that she's given herself a complex, or she is so large as to not fit through some doorways, it doesn't affect everything. When she's hanging out with her girls or her boys, having a laugh, she's not a fat chick. She's just a girl, like any other. If she's a no-nonsense CEO, nobody cares that she's fat, they're just trying not to screw up and get they're heads chewed off.
It's important not to try to bring in character size, or any other trait for that matter, where they have no implications.
I hope that if you're writing a fat chick now or at some point in the future, this post will help.