Beauty and the Beast
Let's start with the most obvious one, Beauty and the Beast. This has been set up from the very beginning as their dynamic.
Red Like Roses - Black the beast descends from shadows/Yellow beauty burns gold.
Their original placements, based in Red Like Roses, are Blake is the Beast and Yang is the Beauty. As the series progresses, Blake becomes the Beauty and Yang becomes our beast. Blake's outfit became more elegant, long jacket, high boots with bigger heels, the nicer top, etc. Where Yang's became bulkier, duller, and covers more.
In the Volume 1 commentary, Miles Luna mentioned that they gave Blake a candelabra (referencing Lumière from the Disney version of BatB) in order to surround Blake with more "Belle-like" items.
The arm that Yang lost is the same one the Beast gets injured protecting Belle in the Disney version of BatB.
At the end of the animated BatB, the Beast says "you came back" to Belle in complete disbelief.
Both girls, while playing the Beast, have a rose. While Blake's 'rose' (Adam) is closer to the Disney rose (enchanted, wilting) and is the reason for her being so standoffish and cold, Yang's 'rose' (Ruby) is closer to the original which just happens to be a rose in the Beast's garden that he's protecting (because it belongs to him).
In a 1946 production of Beauty and the Beast (originally La Belle et la Bête) Beauty has a friend named Avenant (perhaps the basis for Gaston?) who's feelings she reciprocates. She refuses his proposal though in order to take care of her father, who gets taken by the Beast for trying 'steal' a rose from his garden. Beauty takes her father's place yada yada yada, and in the end the Beast transforms into the Prince...who is played by the same actor as Avenant. Which apparently Beauty tells him is a transformation she'll have to get used to.
Our Beauty (Blake) has a 'friend' (Adam) who's feelings she reciprocates but leaves in order to protect herself. She meets our Beast (Yang) through our Rose (Ruby). In Volume 3 when the girls vacillate Blake to Beauty and Yang to Beast, Blake recognizes Adam in Yang. A lot like the 1946 production.
Light and Dark
Another obvious bit of symbolism: light/dark.
Blake is the shadows, the dark, black. Red Like Roses, From Shadows, Wings, Like Morning Follows Night, BMBLB (which in my personal opinion is being sung by Blake), and All That Matters all liken Blake to shadows, see her as being in shadows, or liken her to the dark or the night. Her entire thing is being kind of a dark, subdued character.
Yang on the other hand is the light, the day, fire, yellow. Red Like Roses, I Burn, Gold, Armed and Ready, and Ignite all liken Yang to burning, fire, the sun, etc. Her name literally means "Sunny Little Dragon".
Their colour palettes (Brown-Yellow-Orange and Black-White-Purple) are even warm colours v cool colours.
Yin and Yang
This entire thing is gonna be lifted from sir-adamus
Blake and Yang contrast and compliment each other, just like Yin and Yang should do.
Yang theming is the sun (her name), she's bright, she's happy, but she has a darkness she keeps locked away (that she willingly shares with Blake in Volume 2, Chapter 6: The Candle).
Blake on the other hand is the shadows (her semblance), she's darker, troubled, but she has a lighter side that Yang brings out (in the Volume 2 commentary, Gray confirms this).
Extra Little Things I Really Like
Their eye colours match the other's aura (Blake's aura hasn't been confirmed to be purple yet but....it makes sense thematically), and their aura is their soul. They're like...literal soulmates.
In Volume 5, upon seeing Blake again, Yang is suddenly willing to give up her arm for the sake of the mission. Someone said it might be because the thing she was actually upset at losing (Blake) came back...
Instead of staying in her own room with her theme colour at the end of Volume 3, Yang stays in the guest room of her home which is decorated in purple.
As time has gone on, Yang has incorporated a more Blake-like purple to her outfits. Blake has begun incorporating gold into her own.
(This is more of a joke) Yang's new character song is Ignite, and in This Time (From Shadows Part 2) there's a line "Out of the ashes, a new flame ignites".
In Yang's songs she has a lot of flight imagery.
I Burn:
"Bringing out your rockets? Well, shoot 'em up baby
High as you can go but I'm the one who's gonna soar!"
Gold:
"Love's around you;
In time, you'll fly"
Armed and Ready:
"No more crying
It's time for me to soar!"
And then in Wings we have this:
"Dry your eyes now baby,
Broken wings won't hold you down,
You'll take flight soon baby..."
A sped up version of Wings also plays in the moment when Blake and Yang first see each other again. So that could mean Wings is a Bumbleby song.
Both of their emblems resemble flames (Yang's is a burning heart where Blake's is a stylized Belladonna flower).
If I'm right about the singers of Wings and BMBLB then Yang and Blake both have songs in which they call the other one baby.
Chrysanthemums are often used to showcase love, both platonic and romantic, and yellow chrysanthemums in particular mean neglected love or sorrow. There is no meaning I can find for orange chrysanthemums, but yellow is a colour attributed heavily to Yang.