(Mostly from http://www.etymonline.com/)

Finite comes from Latin for "boundary."

"In-" as in "infinite" means "without," so "infinite" is "without boundary."

"-tude" as in "infinitude" is "state" or "state of" so "infinitude" is "state of infinity"

"-y" as in "infinity" means "quality or condition or state"
(etymology 3 at http://en.wiktionary.org/wiki/-y)

So "infinity" is "state of being infinite."
Same for "-ness."

Apparently, neither "-y" nor '-ness' is Latin. (Not that I care - just observing.)

However, I'm not sure where "-esimal" comes in. "Infinitesimal" was coined (according to the refs and what I've heard) by Leibniz. Seems to mean something like "part of." So infinitesimal could mean "infinith part of" which seems to fit.

Any ideas?