Onee-chan no Stalker

The protagonist, Ayaha, is an ordinary, earnest girl, unlike her talented and popular older sister, Miu. One day, she witnesses a mysterious handsome man named Ren, who Miu had helped in the past, stalking her sister...! However, despite being extremely high-spec, Ren is a weirdo who worships Miu as a "god" and wants to "stalk her all day long to protect her so she doesn't get into any danger"...!? Ayaha is wary of any strange bug (Ren) getting close to her beloved sister, but does Ren care about her too...?

(Source: Hakusensha, translated)