I can find some parenthetical reference to children and even infants being sacrificed to Tlaloc either at the Templo Mayor or on hills surrounding the city, but nothing else. How frequent were these sacrifices? Were they performed in the stereotypical Aztec style (stretched across a stone, heart cut out, thrown down the steps) or was there a different ritual? How old were the children being sacrificed?
Conversely, what is the likelihood that these events were invented by the Spanish to paint the indigenous populations as barbarians?
I'm going to quote the relevant bit from a previous answer of mine. Please let me know if you have any follow-up questions.
Finally, the Aztecs did not invent human, or even, sacrifice in Mesoamerica. As far back as the Olmecs -- more than 2000 years before the founding of Tenochtitlan -- evidence for for autosacrifice is surmised from the presence of ritual bloodletters which an individual would use to pierce themselves. The archaeological site of El Manati has also yielded some rare osteological remains from this era in the form of infant bones, whose archaeological context suggests the remains resulted from sacrifice. Although human sacrifice was practiced by the Aztecs on a scale not before seen, human sacrifice, and child sacrifice, has a history that stretches into prehistory in Mesoamerica.
For child sacrifice, the longevity of the practice may be surmised as resulting from the association with Tlaloc, a rain/storm/water god with incredibly deep historical links in Mesoamerican culture. Miguel Covarrubias famously charted the evolution of the iconography of Olmec Rain God C (we do not know the names of the Olmec deities) along multiple lines in various regions as Tlaloc, Chaac, Cocijo, etc. Covarrubias' artistic hypothesis is not without criticism, but we can see a long standing tradition of child sacrifice associated with a rain/water deity.
For the Aztecs, there was really only one ceremony that focused on child sacrifice, that of the first "month"^3 of the year: Atl caualo/Quauitl eua (both names are given in Sahagun's work). The festival of that month specifically honored Tlaloc, which makes sense given the climate of Central Mexico which, although it is highland and thus temperate (the Aztecs did not live in the jungle), was still subject to tropical rainfall patterns. This meant a wet season/dry season pattern, with the end of the dry season falling around February/March... right when the first month of the xiuhpohualli began.
Putting the pieces together, the rain/water god associated with child sacrifice had his festival right when the climate hit its driest period, and then began to shift back to spring rains and summer deluges. The metaphysical connection should be obvious, but the question of the association with children remains. Unfortunately, there's no satisfactory explanation for the child association other than a seemingly arbitraty association of Tlaloc with helper minor gods (tlaloque) who are often depicted as dwarfs or otherwise as small people.
To return to our misconceptions of Aztec sacrifice being arbitrary and random, this was not simply snatching babies out of their mother's arms and dashing their heads against the rocks. Sahagun describes the ceremonies as such (using the language of "paying a debt"):
And there they left the children known as "human paper streamers,"^4 those who had two cowlicks of hair, whose day signs were favorable. They were sought everywhere; they were paid for.^5 It was said: "They are indeed most precious debt-payments. [The Tlaloque] glady recieve them; they want them. Thus they are well content; thus there is indeed contentment." Thus with them the rains were sought, rain was asked....
And all [the sacrifices] went [to the places of sacrifice] with their head-bands. They were crammed with precious feathers; they had sprays of precious feathers. Their greenstone necklaces went with them; they went provided with necklaces -- they went provided with greenstone bracelets. They had their faces liquid rubber painted; their faces were painted with liquid rubber; their faces were spotted with a paste of amaranth seeds. And there were their rubber sandals; their rubber sandals went with them. They all went honored; they were all adorned, they were ornamented with all the valuable things which went with them. They gave them paper wings, they were of paper; they each had paper wings. In litters were they carried; they went housed in precious feathers, there where each of them customarily went. They went sounding flutes for them.
There was much compassion. They made one weep; they loosed one's weeping; they made one sad for them; there was sighing for them...
And if the children went crying, if their tears kept flowing, if their tears kept fallin, it was said, it was stated: "It will surely rain." Their tears signified rain. Therefore there was contentment; therefore one's heart was at rest. Thus they said: "Verily, already the rains will set in; verily, already we shall be rained on."^6
So, to answer your question, child sacrifice among the Aztecs was a deeply rooted cultural practice associated with a particular ritual complex around a deity of rain and water, to whom humanity owed a blood debt, as it owed a blood debt to all of the divine. That deity's ritual observance was further tied into the realities of wet/dry tropical climate. The practice was further elaborated on by a cultural tradition of associating children with minor deity helpers of that rain/water god.