Weiss makes up the W in Team RWBY. A spoiled rich girl who's the heiress to the Schnee Dust Company, the largest manufacturer of Dust. That's not all she is though.
Weiss is an exceptional fighter, trained by her military operative sister, Winter. Growing up as the heiress to a dust company, her use of dust in combat is exemplary. Her fighting style is elegant and graceful, taking on ballet and fencing maneuvers.
Weiss was born in Atlas, which is basically like The Capital if you're familiar with Hunger Games. Her family consists of her abusive father and current owner of the company, Jacques, her alcoholic mother, Willow, her militant but caring older sister, Winter, and her snobby little brother, Whitley.
The Schnee's are representative of the Four F's of Trauma. Jacques is the cause of the trauma. Willow is "Freeze", using alcohol to dissociate from the world around her. Winter is "Flight", running away to join the military, leaving the Schnee family behind. Weiss is "Fight", needing to aggressively defend herself at every turn until she finally found a safe place among her team. Whitley is "Fawn", doing everything his father asks without question and being the person his father wants him to be, pleasing him as to not incur his wrath.
Weiss' weapon is a multi-action dust rapier named Myrtenaster. Above the hilt is a cylinder that holds dust rounds, letting her infuse her attacks with different elemental effects. Often times, Weiss will use her rapier as a wand, directing her glyphs to perform her desired effect like shooting fireballs or moving her glyphs around.
Weiss' semblance is called Glyphs. She has the ability to create glyphs that have a snowflake motif, and they can do different things. She can infuse her glyphs with dust, creating elemental attacks. Her glyphs can be used as platforms and barriers, allowing her to move around the battlefield in unique ways. Her semblance also allows her to summon the things she's defeated, making them work for her.
Schnees are unique in that they have a hereditary semblance. Willow, Winter, and Weiss all have the ability to use glyphs and summon their defeated foes; Whitley will probably have this semblance if he ever unlocks it.
Admittedly, I was not a huge fan of Weiss at first, but I don't think a lot of people were. All we really knew about her was that she was a spoiled rich girl. I mean, you could read into her trailer song, "Mirror, Mirror", but at the time, I didn't. I didn't really connect that the songs were so important to characterization. She got a bit better by the end of V1, but V2 is where I noticed that there was way more to her. After contacting the Schnee Dust Company for records regarding dust robberies, the receptionist who helped her asked if she wanted to be patched through to her father. Weiss politely said no, and after the call ended, Weiss' "corporate smile" dropped. At that point, I was like, "oh shit there's something up with her family."
V3 is where Weiss became a Best Girl. You learn that her behaviors were because of her strict family, namely her father. We start to see Weiss as the caring teammate she is. She even sacrificed herself during her 2v2 battle against Atlas so Yang wasn't taken out.
Weiss can be snobby, but these are all learned behaviors that she's trying to change. Over time, her snobbiness became part of her charm because now, she was no longer using it to look down on people. She started to care about those around her, and she came to care about the Faunus, something she had a hard time with due to her upbringing.
Weiss is a good example of character development. She such an important part of Team RWBY, and she contrasts with the other girls so well. I've grown to really love Weiss just as much as the rest of the girls.