I stumbled across a gif showing the languages of the region, and to my knowledge these also correspond with the borders of the Kingdoms in Spain to a degree.
Why is it that the kingdoms all grew north-south; surely it would have been logistically easier (and therefore politically easier) to manage and defend a kingdom that was more (for lack of a better word) circular?
Roughly, because the Reconquest proceeded from the North to the South.
If you look at a physical map of Spain, there are mountains running all the way along the northern fringe of the peninsula (the Pyrenees and the Cantabrian mountains). After the Arabs overran the peninsula in the 710s, they failed to occupy that useless northern fastness. That provided a sort of a refuge for Visigoths and the local tribes (Asturs, Basques, etc). From these initial foci of resistance they started expanding south, taking over land and repopulating it (see this [recent comment] (https://www.reddit.com/r/AskHistorians/comments/5idk95/were_there_muslim_minorities_in_the_christian/dbemtg7/?) of mine on the need to resettle the new lands as their utmost priority).
Left to right, you've got the Asturo-Leonese kingdom (Galician and Leonese languages), Castile, Pamplona (Basque), Aragon and the Catalan counties. Even though these kings and counts were as eager to fight each other as they were battling the Moors, most of the territorial gains they had were to the south. From the 12th century the various Christian kingdoms started dividing the yet-unconquered Moorish lands between them. And this, with Castile and Aragon eventually cutting off the Basques from any expansion to the south (I talked about it [here] (https://www.reddit.com/r/AskHistorians/comments/4iu14t/why_didnt_the_basques_conquer_south_during_the/d32a995/?) was what ultimately defined the linguistic makeup of the peninsula. (Well, that and the patterns of colonisation in the lands conquered by the Crown of Aragon, with different lands settled by either the Aragonese or Catalans).
Hope it helps