Didn't it have to do with something about only the fittest being sacrificed? So weak or small individuals wouldn't be able to make it up there (though children were also sacrificed). It is said that they were volunteers, but others doubt that.
Ritual combat was also practiced at the top. The obsidian sword they used was a question on here. There's a legend of a warrior that was killed up there but not before he killed all (or almost all?) of his opponents. I forget the particulars, but it had something to do with the manufacture of his sword/club.
The military connection to the sacrifice was that captives were often sacrificed. That being said, captives weren't the only ones sacrificed. You may be on a feature of pyramid design that I'm unaware of, but the only reason for the steepness of the steps I've ever heard or read was for the improvement in moving bodies to the bottom. Seems reasonable to me that keeping your god fed provides you victory and domination over your neighbors. It is a huge big burning thing in the sky after all, so ... why not?
The extreme-level sacrifice that we think of when pondering Aztecs was a, relatively, recent development. When I say recent, I mean relative to when Cortez arrived. Tlacaelel, an important imperial vizier-like individual, restructured the Aztec pantheon. Tlacaelel raised Huitzilopochtli to the preeminent position in the hierarchy, a move consistent with the Aztecs’ push toward militarism at the time. Huitzilopochtli needed very regular nourishment (tlaxcaltiliztli), which was freshly harvested human hearts. Being “people of the sun,” the Aztecs were responsible to provide old Huitzilopochtli with his very favorite Atkins-friendly meal. The sacrifices were, as I understand it, more often than not sourced from people who were not “of the sun.” The Tlaxcalan people, Aztec neighbors, provided the lion’s share of those sacrificed. As you can imagine, if you lived in Tlaxcala you probably hated the Aztecs. This made the Tlaxcalan people ripe for the picking for Cortez and we all know how that worked out for old Montezuma.
Just as an aside, the common consensus seems to be that the Aztec empire crumbled under the combined force of colonial subjugation and imported European diseases (mostly smallpox). There is evidence that there was already a demographic crisis based on all this human sacrifice before the Spanish arrived that would have toppled the Aztecs without European intervention. No way to know that one way or the other, but all the indignation over how they were treated by the Conquistadors when they were doing their own mass killings is, at the very least, ironic. I'm not saying if I were an Aztec I wouldn't be pissed at Cortez, but they were killing their own people and neighbors at an alarming rate. Just sayin ..