The tale "The Smallest Dragonboy" has Keevan, a boy who is shorter than the other candidates (and is teased about it relentlessly). Keevan's always been a good student during his training sessions, but his size downgrades his chances. Keevan is badly injured by his arch rival (and all around Jerk Ass) Beterli. While he recovers he's assured that he will have other Hatchings. Despite everything, Keevan manages to find his way to the Ground and Impresses a large bronze dragon named Heth.
Even more touching in that he'd nearly missed the Hatching because of his injury, and staggers onto the sands to find all the eggs hatched and empty. Then Heth, whose egg Keevan had made a special point of touching, nudges him from behind. The hatchling bronze had refused all the other boys and waited for him.
Keevan shows up in one of the later novels as a capable Weyrleader, and apparently more than caught up to his peers in physical size.
In The White Dragon, when Robinton suffers his first heart attack the nearby dragons contact him telepathically and force him to stay awake until medical help arrives, sensing that if he allowed himself to sleep he would die. The dragons know who their friends are, even those who aren't dragonriders.