Origin of the term "Resident"
Robin Linden stated in the official forums:
It was pretty early in the development of Second Life. One of my jobs was to come up with the different words we wanted to use, including the name! The naming discussions were usually between me, Philip, Hunter and Peter (both of whom aren't here any more) with feedback from everyone else.
When it came to what to call the people in the world, we knew we didn't want to call them 'users', although that would be the most typical thing for software. However, the word 'users' doesn't do a very good job of describing the two-way nature of Second Life, where the people involved are providing content and contributing to the experience.
We also thought about 'members' (boring!), 'citizens' (too political!), and 'players' (too game-y).
'Residents', however, seems most descriptive of people who have a stake in the world and how it grows.
– Robin Linden, 2006/07/31, SL Forum
"Resident" is frequently capitalized because it's used as a title by habit. However, given a changing, growing world, the Doc Team is evaluating (as of 2009-02-01) whether this still makes sense.
First use of "Resi"
Torley Linden (formerly Torley Torgeson) is the first known person to abbreviate "Resident" as "Resi", dating back to 2005-10-06. Over the years through repeated usage, this shorthand gained popularity both inside Linden Lab and publicly:
I joked in an email to Philip that "Resi" takes the "Dent" out of "Resident".
– Torley Linden