Beady-Eyed Loser

Bob is an Unlucky Everydude, the classic underdog. He's a terrible student and a klutz on the field. He can't be an underdog if he's attractive to other people, so Alice will occasionally comment that he's not much to look at. You don't see what's so ugly about him, but it's an Informed Deformity and maybe he's Hollywood Homely. Then at some point in the story he meets Charlie, the in-universe stud of the show whose beauty is admired by all (especially Alice). There's one problem, though. He really isn't any more attractive than Bob. That's odd...

Due to Generic Cuteness, Only Six Faces and possibly Beauty Equals Goodness, it can be very difficult to differentiate an average or even ugly looking character from a beauty, with the only truly unattractive characters being Gonks. This can make it especially odd when the supposedly average-looking main character meets the in-verse Bishonen of the show, and you realize the only real difference between them is the hair cut and maybe some bishie sparkles.

So how do you tell the audience the character is supposed to be average or unattractive while still making them easy on the eyes? Make their eyes beady. It's not that beady eyes are really all that ugly (just goofy looking), but in a world where beautiful doe eyes are the norm, it sort of makes sense that this character would be considered unattractive in comparison, even if they otherwise look like everyone else.

To summarize, these type of eyes are a visual cue that the character is a loser or outcast, and obviously they'd be considered unattractive by their peers. If this character is a main character or even given some time in the spotlight, their eyes will be less beady during serious moments or if they show personal growth.

Compare and Contrast with Face of a Thug, since they too have beady eyes, though those elicit a different reaction.

Anime and Manga

 * Simon of Tengen Toppa Gurren Lagann was considered gross and weird by the girls of his village, though that's probably more to do with the amount of time he spends digging. The Black Siblings also considered him completely unremarkable, especially in comparison to his big brother figure and hero (who, to be fair, was a Hot-Blooded Walking Shirtless Scene.)
 * Paralleling his growing confidence as he matures into a man, his eyes becomes less beady throughout the story, and by the end, resemble Kamina's.
 * Sena from Eyeshield 21 spent his entire life being pushed around by bullies, and started the story with very beady eyes (practically dots). By the end of the series, Sena's eyes are more normal looking.
 * Tsuna of Katekyo Hitman Reborn starts the series as a stereotypical loser complete with the beady eyes to match. As the story progresses, he not only experiences personal growth and many power upgrades, but somehow goes from beady-eyed to moe-moe. Though that's probably more to do with art evolution, as everyone in the story gets more and more pretty.
 * Shikamaru of Naruto graduated second worst of his year, and is assumed to be a lazy loser till people discover he's got an IQ of 200.
 * Ataru of Urusei Yatsura is one of the unluckiest and perverted characters in the Rumiko Takahashi universe...He's also the most beady-eyed.
 * Kai Shiden of Mobile Suit Gundam is a Lovable Coward who chases skirt and snarks on the relatively inexperienced commander Bright Noah. In a subversion of the usual formula, he retains his beady eyes even when he develops into a combination Adventurer Archaeologist-Intrepid Reporter in Zeta Gundam.
 * Hideki from Chobits, big time. He's a broke, spastic, computer-illiterate ronin who couldn't talk to a girl or get into college to save his life.
 * Yuuji from Tona Gura. It's parodied in that when he tries to look chivalrous, his eyes adapt the "regular anime" style.

Western Animation

 * Gus Griswalde from Recess is the shy Lovable Coward who just moved to town. He's the only member of the regular cast with Black Bead Eyes.
 * Snips and Snails from My Little Pony Friendship Is Magic.