Since their contribution was crucial to defeat the Aztecs, did the Spanish respect them more?
The Tlaxcala received some special rights under Spanish rule that other peoples did not enjoy. They were promised not to have their lands seized, nor to be taxed by Cortez, both of which were at first respected. The Tlaxcalans also aided the Spanish in their conquest of other states, including in the Mixtec Rebellion (1540-41) and the Chichimeca War (1550-90), which they afterwards helped settle.
These rights were extended after 1585, when Diego Munoz Camargo's Historia de Tlaxcala was shown to the Spanish king Philip II. The book detailed the history of Tlaxcala with rich illustrations, especially focusing on post-colonial history. The purpose was at least in part to make the Tlaxcalans appear better in the eyes of the Spanish - Spanish-Tlaxcala conflicts were downplayed or ignored, Spanish conflicts with other states were overstated and the Tlaxcalans were portrayed as being more enthusiastic about Christianity than they were when they first encountered it. It is also a valuable historical document that portrays Tlaxcalan history, customs and culture though.
In 1591, Tlaxcala settlers were granted further rights, so they could be used to peacefully colonize other tribes, by having them settle among them, thus allowing them to be introduced to a peaceful, agricultural, Christian lifestyle. These settlers gained some special rights, such as being exempted from Spanish taxes, getting control of various Chichimeca resources, property rights of the land seized from the Chichimeca and being allowed to ride on horseback and use guns. These Tlaxcalan settlers settled among other places along the Rio Grande.
It worked, at least for a while, though later the Spanish Crown extended control over the New World in an effort to squeeze more profit out of it. The Tlaxcalan special rights were gradually eroded.
The Tlaxcalans were not immune to smallpox and other epidemics either. Combined with emigrations and the construction of a canal to drain the valley of Mexico, the city state of Tlaxcala was almost wiped out - according to a 1625 document the population had declined from 300.000 in the sixteenth century to a mere 700 then.
Sources:
http://special.lib.gla.ac.uk/exhibns/month/jan2003.html