Blazon: Per bend sinister azure a crown proper and or a croizer in bend sinister surmounted by a mitre purpre, all within a bordure gules charged with sixteen bezants
The name of the town evidently derives from avia, Latin for “grandmother.” This is apparently in reference to the antiquity of the town, which was well established even before Reconquista. I don’t have much in the way of information on the arms, but it seems reasonable that they’re at least partly canting – obispo is “bishop” in Spanish, and the mitre and croizer are essential parts of a bishop’s regalia. (Also, the name of the town might translate to something like “the bishop’s grandmother, which amuses me.) There’s a slight possibility that the bezants were intended to represent some of the archaeological finds in the area, which include gold rings and several coins, but it’s a very slight possibility.
Blazon: Per fess argent a cross of Calatrava gules and of the last, thirteen bezants in pale 4, 5, and 4.
Okay, first of all, about the eyes: they are not actual eyes. They are the sources of the Guadiana River, which are located near the town. Those get their name from a mistranslation from the Arabic: ﻋﻴﻦ can evidently mean both “eye” and “spring,” and whoever did the translation to Spanish picked the wrong one.
The cross of Calatrava is probably due to the fact that the town was granted to the Order of Calatrava in 1466. That was also the same year that the Grand Master of the Order, Pedro Giron, died suddenly in Villarrubia on his way to marry Princess Isabella – yes, that Princess Isabella, the one who ended up marrying Ferdinand II of Aragon and becoming Isabella I. Maybe it was a very odd way of expressing condolences? The bezants are attributed to the Counts of Salinas, who purchased the town in probably the early 16th century. I did find a record of at least one family with that surname using roundels in a similar arrangement, so it’s not completely out of the question.
Arms of Alan la Zouche (1205-1270) and Ellen de Quincy (?-1296)
From p81 of Lacies Nobilitie by Sir John Ferne (1586)
Blazon: Per pale baron and femme gules thirteen bezants 4, 3, 3, 2, and 1 and a canton ermine and gules seven mascles conjoined or 3, 3, and 1
The la Zouche arms have virtually always involved some number of bezants, but how many depends greatly on the source. The most common is probably ten in pile or 4, 3, 2, and 1, but thirteen or fourteen also occur, and some authorities simply describe them as bezanté, or deliberately unspecified.
Blazon: Argent on a cross flory sable between in chief dexter two swords in saltire and sinister two keys in saltire, both azure and gules, five bezants
Crest: On a mural crown or a fountain between a branch of oak leaved and fructed and a branch of beech slipped proper
Supporters: On the dexter a lion sable and on the sinister a horse argent each with a cross formy fitchy pendant from a collar counterchanged
Mantling: Sable lined argent
Motto: Ad summa nitamur (Let us strive for perfection)
The cross flory comes from the arms of John Whitgift, Archbishop of Canterbury, by way of the County Borough of Croyden. The keys and swords refer to the Abbey of St. Peter and St. Paul. The fountain symbolizes the source of the River Wandle, and the white horse is from the arms of the Earls of Surrey.
Blazon: Per quarterly I gules five bezants in saltire, II azure two arrowheads in fess, points to the dexter and sinister, surmounted by a castle triple-towered argent, in chief a garland proper; III or a lion rampant gules; IV argent three men on a bridge supporting a log in bend sinister, all proper