I wrote about Spanish influence on Tlaxcala and other indigenous groups in central Mexico before, e.g. in some detail over here. Since that answer is more general I'm adapting and extending it here specifically to focus on Tlaxcala. As the Spaniard's main ally during the defeat of the Aztec Triple Alliance, Tlaxcala received special rights and privileges from the Spanish Crown: So less "spoils of war" than important judicial privileges. They were far from the only Nahua (or native) group to be rewarded in colonial times - the Mexica, former leaders of the Triple Alliance, are another famous example. But they did reach quite a unique status, including city and encomienda rights. All this was tied up with the long-lasting Tlaxcalan history writing, in which their position and special allies and Christians was highlighted throughout colonial times.

Tlaxcala's special status was connected to the Tlaxcalans being very early and important allies of Cortés. But it also had much to do with colonial machinations of the Tlaxcalan native elite and its cabildo. Peter Villella has stressed how a narrative of Tlaxcalan 'exceptionalism' was strongly pushed by its nobility. This included regular travels by its members to the royal Spanish court (e.g. By the historian Munoz Camargo and consorts) ; funding for religious institutions ; and the financing of chronicling of the Tlaxcalan « conquistadors » via (graphic) mapas and (written) chronicles. Following conquest the major rôle of Tlaxcalans in the conquest or Northern Mexican regions was also increasingly highlighted. Villella also shows some interesting parallels with another region, where the Otomí 'conquistadors' were highlighted and granted privileges as a consequence.

All such endeavors paid off : Tlaxcala was the first city to be officially awarded the status of city with its own sigil. Even more importantly, Tlaxcala was not made into an encomienda, and received royal assurances that Spaniards should not move to its territory. This accounts for the comparatively smaller rôle Spanish or creole people played there in the first 100 years following conquest; connected with this we see a tradition of annals writings over centuries in Tlaxcala, when these writings had already « died out » in Mexico city. It also meant that the new city Puebla that was open for Spaniards and others had to be founded outside of Tlaxcala.

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While Tlaxcala surely reached a special status, the Spaniards did not hold their pre-conquest agreement with them fully. This agreement had promised Tlaxcala control over Huexotzinco, Cholollan, and other former allies. This raises the question of why the Tlaxcaltecs didn't „rebel“ against the Spaniards. One possibility is that they expected to still profit from the continued alliance – which they most definitely did in many other ways. Another is that they also calculated it too risky to try and take over dominance over all other population groups – keep in mind that it decades for the Triple Alliance to succees as it did; and that although Tlaxcala successfully resisted the Alliance, they did not manage to defeat them neither. So (for them) it would have been far from a safe bet to try this now with many still powerful other native groups in position... and with quite a lot of political chaos after the fall of Tenochtitlan.

Villella (in his article „Indian Lords, Hispanic Gentlemen“, p. 4) sums up Tlaxcala's special status succintly:

Tlaxcalans were famed in New Spain as the primary native participants in the 1521 defeat of Tenochtitlan, the dominant power of pre-Hispanic central Mexico. Thus, colonial Tlaxcalans tended to remember the conquest in tri umphant terms: for them, it was as much a Tlaxcalan as a Castilian achieve ment. The result was a unique ethnopolitical identity that Jaime Cuadrillo has named tlaxcaltequidad-. a self-understanding rooted in the idea that Tlaxcalans, as willing Christians and participants in the Spanish conquest, were not defeated subordinates in Catholic New Spain but rather its victorious archi tects.

This discourse allowed them to lay claim to a comparatively high degree of local autonomy and ethnic dignity within the Spanish crown. While Tlaxcala was not the only native polity to have aided the Spanish conquistadors, it was among the most successful in ensuring returns on its original investment in Spanish imperialism. While the earliest iterations of tlaxcaltequidad date to the immediate postcon quest decades, local leaders such as the Salazars sustained it to the end of the colonial period. Along the way, the discourse accumulated ever more legends, flourishes, and icons. A growing array of royal privileges and a series of divine miracles, they argued, attested to Tlaxcala's singular place in the eyes of both God and kin.

All this was also tied to an especially strong native Christianity in Tlaxcala – The introduction of Christianity in Mexico since the 1520's being another major force of integrating native groups into the colonial system, which I didn't really mention above. So I would say that in the 1520s Tlaxcala had two options: A risky war with the Spaniards, whom they had experienced as strong opponents even with fewer native allies, who now had other strong allies beside Tlaxcala behind them, where success was far from sure; and even in case of success they would have had to still defend their dominance against various other groups. And second, keeping their alliance and building on their successes to receive a very special status protected by the Spanish.

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To give you another example of how Tlaxcala evolved in colonial times from the later 17th century, the writings from Don Juan Buenaventura de Zapata y Mendoza are an interesting source on this. Zapata y Mendoza came from an important noble familiy and held held posts in the cabildo over decades. Here we can still see the practice of « rotating » the major council positions between a specific group of native nobles that was common in precolonial polities or "altepetl". In his annals he underlined the special status of Tlaxcala as an altepetl that was never conquered (neither by the Aztec alliance nor by the Spanish).

He also highlights the continuing importance of the altepetl structure for Tlaxcalan society and culture. So he described the traditional rotation between the four sub-altepetl, and mentions many Catholic processions, that however showed respect to the altepetl's four corners (as in pre-hispanic traditions). What is more, Zapata also shows how other non-native groups like Spaniards or mestizos play increasingly bigger roles in cabildo affairs. This includes Spanish gobernadores who change traditional customs – and disrupting the traditional major influence of native nobility so central to an altepetl's continuation. In this light we can maybe understand the ire of the noble Zapata y Mendoza when a 'mestizo' was elected governor for the first time:

[…] the infernal mestizo governor don Nicolás Méndez […] : at his hands were destroyed the inherited privileges of the pipiltin, the right to show appreciation to the viceroy when he came here.That one, he destroyed everything, the right to go on procession on the altepetl's feast day, or major holidays, or at the proclamation of bulls in Puebla. It was his fault, and that of the [Spanish] tlatoani who used to be here, don Juan de Echeverría and his wife doña Francisca de Sosa. […] He asked to get in so that he would be governor here in Tlaxcala forever, that mestizo from hell.

To conclude then, Tlaxcala managed to hold on to its special status throughout the colony. Their specific rights however evolved over time, and by the turn of the 17th century there was increased infuence of Spaniards, mestizos and other groups in Tlaxcalan politics and economy. While this meant in certain ways less prestige and riches for native Tlaxcalan elites, we have native history writings from the region at least into the 17th century - showcasing the continuing influence of a native discourse of a Tlaxcalan singular status or "tlaxcaltequidad". How the different native groups in central Mexico - allies or enemies of the Aztecs were rewarded post-conquest depended on a host of factors. Important ones include a given group's distance from colonial power centres, and pre-Hispanic influence. In any case there were quite a few cases of groups continuing or even expanding their influence, including the Tlaxcalans and Mexico. But in numerous cases, including the formely influential Acolhua, the elites' influence would increase to the point that they held little to no power by the later 16th century.

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• Villella, Peter: Indigenous Elites and Creole Identity in Colonial Mexico, 1500-1800

• Peter Villella: Indian Lords, Hispanic Gentlemen. The Salazars of Colonial Tlaxcala (Nice article on one noble Tlaxcalan family, the Salazars, who managed to conserve and even broaden their priviliges in colonial times, it's on project muse)

• Charles Gibson: Tlaxcala in the Sixteenth Century

• Lockhart, James (ed.): The Tlaxcalan actas : a compendium of the records of the Cabildo of Tlaxcala (1545 - 1627)

• Zapata y Mendoza, Juan Buenaventura: Historia cronológica de la noble ciudad de Tlaxcala

Edit: added sources