The flip side of this question is why so many Mesoamerican groups ("tribes" is not appropriate here) wanted to use the Spanish, and probably one that has more explanatory power and has its roots in the political situation of the time.
The nature of the Aztec state was primarily extractive. The triple alliance of Tenochtitlan, Texcoco, and Tlacopan were less interested in directly controlling conquered regions than they were in the having the goods of those regions diverted to their cities. Taking lands for use by Aztecs elite did happen, though more often with the early and close-in conquests, and there are a couple times when they outright razed a rebellious city and repopulated it with their own people. Areas in more border areas, particularly with the Tarascans, also saw more directly control and garrisoning. For the most though, the Aztec didn't care what language you spoke, what gods you worshiped, or who ruled you, so long as it didn't interfere with the regular shipments of tribute to the core Aztec cities.
The rather loose system of control meant rebellions by towns and cities who thought they could slip the yoke of the Aztec tribute system were not uncommon, particularly after the death of a ruler. Hassig, in Aztec Warfare points to the mountainous terrain and the lack of draft animals (thereby necessitating human porters) as limiting factors for long, sustained campaigns and thus more direct control. The Inca, however, with more mountainous terrain and the relatively light carrying capacity of llamas, exercised a more intensive system of rule, so the looseness may have been less a bug and more a feature. It allowed for the Aztec armies opportunity to seize slaves and captives for labor and sacrifice. Hassig notes that the near annual campaigns of the Aztecs often included a stop to quash a wayward town on the way to a new area (though he also posits that some of these might have been more "symbolic" conquests -- a brief show of force to re-affirm the tributary relationship).
Regardless, tributary polities exercised broad discretion over their internal affairs, with the biggest symbol of a Aztec power, outside of garrisons in some areas, being calpixque, essentially tax collectors. It was these functionaries the Spanish, as they made their initial contacts along the coast of Veracruz, reported meeting and learning from them the existence of the Aztec state.
Now, Cortés' account would have us believe that the long-suffering people of Mexico were yearning for a savior to free them from the oppression of the Aztecs. In his Second Letter, for instance, he writes that some of the first people he met in the Gulf regions controlled by the Aztecs:
on hearing from me of your Majesty and of his great and royal state they they declared themselves willing to be the subjects of your Majesty and my friends, begging me to defend them from the lord who ruled them by force and tyranny, taking their children to kill and sacrifice them to his idols and giving them other grievous causes for complain of which they informed me.
Of course, it's easy to put some words in the mouths of anonymous peasants. Meeting the ruler of a town, which "both bore the name of Caltanmi," on his journey inland from the coast, Cortés found those with an interest in remaining on the right side of the Aztecs to bit a bit more reticent. After informing the ruler that the King of Spain was a great and mighty ruler and that all the lands of Mexico were now under his dominion, Cortés asked for a gift of gold as a show of fealty.
To this he replied he had gold but that he would not give it to me without Muteczuma's orders; on receiving such orders, however, he would give up his gold, his person, and whatsoever he had. To avoid any unpleasantness or mishap in my intent or road I spoke him as fairly as I could telling him that very soon Muteczuma would send him bidding to him to give up the gold and what more he said.
Cortés does not say what reaction Caltanmi was to his promise, but his silence strongly implies that no gold was proffered. The incident does, however, illustrate another technique Cortés used extensively during his early ventures in Mexico: Lie. Out of both sides of your mouth. Tell whoever you're speaking to anything that might get them on your side.
So to the emissaries of the Aztecs, Cortés said he was just coming to pay his respects and establish relations between them. To the tribute-paying Totonac lords on the coast, he promised to free them from their obligations to the Aztecs. To the Tlaxcalans he promised to be their closest friend and ally, but that he really did need to continue on to Tenochtitlan; his King had ordered him to, you see, no choice in the matter. He then turned to the Aztecs traveling with them and promised them that his hanging out with the Tlaxcalans was really just for temporary convenience, and that as soon as he got to Tenochtitlan he'd make a real alliance with Motecuhzoma. At one point, early on, some calpixque were imprisoned by the ruler of Cempohualla (at the behest of Cortés, per his own writings), and then Cortés had a couple of them freed and sent back to Tenochtitlan, explaining that he had nothing to do with their seizure and that the Spanish were totally here to be friends with the Aztecs.
Now, whether or not any of local rulers believed the lies of Cortés isn't particularly relevant, because they were all happy to use the Spanish for their own immediate goals. Left out of Cortés' letters, for instance, is an episode that Bernal Díaz del Castillo records, wherein the Cempohuallans told the Spanish that there was no way they could join their cause unless the Cortés could rid them of an Aztec garrison in a nearby town. So the Spanish and Cempohuallan force set out and sacked the town, which turned out to not have an Aztec garrison, but did have a long-standing rivalry with Cempohualla (later in Tenochtitlan, Cortés would pin all this on the Cempohuallans acting alone).
Likewise, the Spanish found themselves in a terrible situation as they crossed through Tlaxcalan lands, quickly beset on all side and in a state of fighting a retreat. Then, all of a sudden, the attacks stopped and the Spanish found themselves approached by emissaries of Xicotencatl and Maxixcatl, the rulers of the two most power cities in Tlaxcala (like the Aztecs, it was not a singular state, but a confederation of closely aligned cities). The Tlaxcalans then convinced the Spanish to take a route into the Basin of Mexico which led them through the city of Cholula.
Cholula (along with a couple other cities) were key centers in an area that had been crossing back and forth between Tlaxcalan and Aztec dominance over the decades, and Cholula had just recently had a pro-Aztec faction take power. Shortly after the Spanish arrived, native informants let Cortés know (via Malinche) that the Cholulans and the Aztecs were planning to launch a surprise attack, and that he should strike first. So Cortés waited until all the key men of the city were gather to bid him goodbye, and then launched a surprise attack on the largely unarmed Cholulan assemblage. Shockingly, a pro-Tlaxcalan faction then took over leading the town; who could have predicted such a thing?