WARNING: The following contains spoilers for My Hero Academia Episode 80, "Relief for License Trainees," now streaming on Crunchyroll, Funimation, VRV and Hulu.
My Hero Academia is, for the most part, a pretty down-to-earth series about teenagers with superpowers. Rarely does the anime venture into anything creepy or weird beyond the expected sort of adventures teenage heroes would embark upon. Therefore, viewers don't expect to watch an episode in which one character watches another while he sleeps, unaware of the watchful eyes outside the glass.
So, when this occurs in Episode 80, one might reasonably ask why Aoyama is watching Deku as he sleeps.
Aoyama Watches Deku as He Sleeps in My Hero Academia Episode 80
In Episode 80, Aoyama offers Deku cheese before lunch -- or, rather, Aoyama feeds the cheese to Deku. That strikes Deku as odd, but not odd enough to cause alarm.
However, when he finds a spread of the same cheese Aoyama fed him outside on his window, arranged to spell out the words "I know," Deku has more than enough reason to actually be alarmed. Aoyama, as it turns out, had been outside his window that night.
Naturally, that freaks out Deku, who's afraid every time he and Aoyama are in the same room. That's despite that, in public, Aoyama acts absolutely normal. Deku has fought villains time and again, but this is too much even for him to handle.
Aoyama's Explanation for Watching Deku Is Actually Wholesome
During a training lesson, Aoyama gets sick using his Quirk, which leads Deku to take advantage of the situation. He takes Aoyama aside and asks him why he was outside of his window the night before.
It turns out that Aoyama had no clue how unnerving his action was; he simply wanted to leave a "surprise" for Deku. Aoyama identifies with Deku because, like Deku, his Quirk causes discomfort when he uses it. On top of that, he needs to wear a device to contain his belly button powers, or else energy will leak from his navel. He has always related to Deku in this sense, and simply wanted to get to know him better.
That, of course, raises the question why he thought leaving vague messages outside Deku's window at night was a good idea. It's possible Aoyama would like someone to do that for him, which invites even more questions about his perspective on human behavior, indicating he has no concept of propriety.
However, it also eliminates any possibility Aoyama did this out of malice. Once Deku thanks him for the surprise, his relationship with Aoyama improves. As the series and manga progress, Aoyama's relationship with Deku becomes more normal. Aoyama expresses concern for Izuku without coming across nearly as creepy. He is the first to notice Deku is having issues in Season 5 when he starts having strange dreams. While Aoyama did watch Deku as he slept, his creepy behavior was actually well-meaning.