During Aztec military expansion, did any other peoples of mesoamerica give them significant trouble militarily? If so, what people and do we know why?

Definitely the Tlaxcalans who were probably one of the biggest pains in the butt for the Aztec Triple alliance and their ambitions in Mesoamerica

In Bernal Diaz Del Castillo's book about the Conquest of New Spain, he references the Tlaxcalans as being quite poor in terms of gold and riches as opposed to the Aztecs but despite this, the Former(Tlaxcaland) was still quite militarily formidable and the Aztecs for all their strength couldn't completely overcome the Tlaxcalans As they did with other native peoples.

The reason was probably the fact that unlike other Native peoples that the Aztecs had conquered, the Tlaxcaland were quite numerous and could field armies that could even match the Aztecs from time to time which was seen when Bernal DiaZ described the encounter between the small Spanish army and a massive force of thousands of Tlaxcalan warriors(estimated by counting the number of native banners), so the Tlaxcaland were no simple push overs.

Like the Aztecs the Tlaxcalans were also a militaristic society who also practiced human sacrifice and by all intents and purposes probably wouldn't sit and roll over to Aztec aggression.

The result of this was more of a stalemate between the two powers as neither one could truly gain superiority over the other, although this stalemate tended to favor the more offensive Aztecs who would still raid Tlaxcalan territory from time to time but couldn't conquer it entirely.

Even so the Tlaxcalans were still a pretty big threat to the Aztecs and a threat to their goal of expansion, so much so that without the aid of the Tlaxcalans, Cortes dream of defeating the Aztecs would've been impossible.