percy didnt turn down godhood for annabeth. he turned around and faced her, and seeing her solidified his opinion. percy didnt turn down godhood for annabeth. she just boosted his confidence to do it.
and that happens a lot. often she'll be the first, or one of the first, to admit when percy has good ideas. she'll be the first to compliment him, she'll be the first to hype him up (unless grovers there)
percy doesnt do everything for annabeth. but when he does do stuff, and he thinks of her, its because she gives him confidence, because shes almost always in his corner, ready to back him up
and typing this i think im realizing why annabeth as percys achillies heel could fit better than sally (something i was a bit on the fence of for a while). the reason being, sally was percys comfort. she was safety, she was home, and while he was fighting for that, he didnt need comfort. he didnt need safety. he needed support, strength, confidence. no im not saying thats the only reason percy saw annabeth when he got the curse, but what i am saying:
annabeth helping lift percy up, comforting him when he needs it like he does for her, them being there for each other, and annabeth never actually insulting him. yes she calls him seaweed brain, but she doesnt think hes stupid. she says it herself in demigod diaries, right here. there arent many cases of this in canon that i can think of, i will admit, where she audibly compliments how smart he is, but thats just one thing. shes very clearly impressed by a lot of the other stuff he does and that whenever percy is being looked down on by someone (ignoring thalia in ttc) she almost always jumps to his defense, and is the first one to do so
she makes him feel like hes not worthless. like he can actually do something, do something good. she gives him confidence to be himself, and in the achillies curse scene, gives him confidence to live and to win a war
he didnt turn down godhood for annabeth, but looking at her made him feel more confident in his decision.