In short, I am unsure how frequent the human sacrifice component of Aztec religion was performed. But it would need to be quite frequent to exceed the suffering caused by the Spanish governing practices in the New World - even excluding suffering caused by introduction of new disease.

Unfortunately this is a controversial subject in academia -- largely because it informs arguments like this one, but also because of sparse primary evidence. I've seen estimates as high as 250,000 sacrifices a year in Aztec-controlled territory, although more conservative figures put the number an order of magnitude lower; I'd probably be more inclined to accept the latter, given the relatively small population of the Aztec states of the time. Aztec use of prisoners of war as objects of sacrifice is pretty well documented (though there's some controversy over the role of the so-called flower wars), but even with that input it seems to me that there'd be some basic sustainability concerns.

I've heard estimates even lower than that, but I'm not sure how credible they are.