Waga Itoshi no Wota Kanojo

Sakai Haruhiko, your average harmless background character, confesses his love to frail resident mysterious cool beauty Shiraishi Yuki. She seemingly turns him down, like all her other suitors, only to accept him as a friend. Though she has a condition that he has to accept her "everything", that being her true neet-ish Otaku-like behavior and mannerisms (like skipping school three days a week with the excuse of a "frail" body) on top of her hyper-dere personality. Now it is up to him to succeed her tests to graduate from friend to (Otaku-)boyfriend.