the century - fighting unit

[D B Campbell]

I believe, if memory serves, (and someone with far better resources than I is going to have to dig deeper into this) .... I believe that centuria come in part from the word centuriationes which are land divisions... related to the word centuriatum

Centuriation doesn't really have anything to do with the army, Sean.
It's actually a surveying term: according to Varro (and Pliny, I think), arable land was divided up into plots of 200 iugera, each of which was farmed by 100 families (i.e., 2 iugera each). (Iugerum refers to a "yoke" of oxen: i.e. the amount of land that a pair of oxen could plough in a day.) Hence, "centuriation" derives from the idea of 100 families (centuria = "hundred").

At some point that group of soldiers was regulated to be a certain size (in our case 80)

You may be surprised to learn that our only evidence for a centuria being 80 men is a statement in an anonymous, undated treatise! (The so-called De munitionibus castrorum of "Hyginus".)