You saved him, he was going to die and he knew it but you stopped Mahito and saved him...Sure the curse got away and both of you were injured but that doesn't change the fact that you saved him, so now...He's attached to you like glue...

Yuji helped him enroll in Tokyo Jujutsu High...Since he's been admitted he's followed you around quietly, even if you don't acknowledge him he leaps at any opportunity to be around you...You're his hero, his light, you see him, all of him and he loves it...