13 percent only? Are the rest just ambiguously brown or forgotten their heritage. I know that tons of Northern Mexican Amerindian groups vanished without leaving a trance of their languages. Zacatecs, Guachichiles, Cazcans, and so on
The large proportion of Mexicans are "mestizo", meaning of spanish and indigenous heritage. There is also a large group of "white mexicans". Of course, Mediterranean heritage is just ambiguously brown enough to be perceived as mestizo too, so i take the proportion of indigenous heritage in the mestizo population with a pinch of salt. The mestizo mexicans appear to suffer from racial inferiority at the moment; whiter mexicans apparently tend to be seen as superior. I highlight this because it just doesn't make sense for a successor state of the Aztecs to discriminate against ethnically Aztec people. Regardless of the depth of truth in this statement, mestizo's are deeply european in their cultural roots. Even if they had a very strong indigenous heritage, they are very clearly absorbed into the europeanised modern mexico now. It has nothing to do with the aztec empire that predated it, their culture, political systems, economy, religion and philosophy have been completely changed.
The large proportion of indigenous people also died after initial contact. Estimates suggest that up to 90% of the population of the americas died from the introduction of european diseases.
Additionally, whilst it occupies the majority of the area the Aztec had within their empire, and the capital is constructed over the old Aztec capital, Modern mexico encompasses a huge area and a great number of indigenous groups. If we're calling is the Aztec successor state we've also got to call it the Tlaxcala successor state, despite the Tlaxcala and Aztecs being contemporaries and basically sworn enemies.
Basically, it is just plain wrong to describe Mexico as a successor state of the Aztec empire.
As to the Aztecs, they're unlikely ever to have formed a substantial population base. They had three cities, all of them less than three centuries old by the time of the Conquest. Mexico likely has a larger Maya population than a Nahua one.
If we take the Aztecs to be the Mexica (which really we should, especially if we talk Alexander as representative of the Greeks as precedent), then they had far more than 3 cities, the Mexica centred in Tenochtitlan formed an alliance with two other Mexica city states to become the "Aztecs" and the dominant Mexica force in the valley of Mexico. Tenochtitlan was a huge city just on its own however, don't be fooled into thinking they had a low population. The city itself was populated only by nobles and individuals of high standing. Beyond the city boundaries there was huge urban sprawl where the more "common" folk lived.