I am watching season 4, when one of Daenerys' dragons burned the goat of a poor shepherd boy. The dragon has grown much in just a year, the previous dragons as told were comparatively weak and smaller. Does anyone know why?
In season 4, it has not been only an year since they were born, rather three to four years. They were born in 298 AC and season four begins in approx. 302 AC, you can see the timeline here. As for why they still grew this big as compared to the last surviving dragons, it is because the last dragons were kept in captivity, whereas Drogon, Viserion and Rhaegal are not (keeping in mind that Viserion and Rhaegal were smaller than Drogon as they were kept captive under the Great Pyramid of Meereen for most of the time).
Season 6 Episode 2
TYRION: Daenerys is the dragon queen. Can’t very well let the dragons starve, that’s obvious.
GREY WORM: If a dragon does not want to eat, how do you force him to eat?
TYRION: Dragons do not do well in captivity.
MISSANDEI: How do you know this?
TYRION: That’s what I do. I drink and I know things.
TYRION: The dragons Aegon used to conquer Westeros ranged over hundreds of miles. Then Daenerys’s ancestors started chaining them up in pens. A few generations later, the last dragons were no larger than cats. They must be unchained or they’ll waste away. Missandei, how many times were you in the company of these dragons?