Maybe the tzvi~tzvi connection began as a pun.
Like saying "my deer wife"?
There's also the Gemara's drash (Kesubos 112a, Gittin 57a), in which the adjective "tzvi" for Eretz Yisroel is taken to mean "gazelle." The points of comparison are: the animal's swiftness (similarly, E.Y.'s fruits ripen quickly); and the fact that its hide shrinks after it's flayed (similarly, the land produces more crops than there's room to store, and it "shrinks" geographically when it's not populated by Jews).
I learned the same concept but from a more optimistic angle: although the land appears small, there is actually room for the entire Jewish nation (i.e. stuffing the deer back into the deerskin).
Kabbalistically, that two seemingly unrelated ideas converge onto one root could hint that something essentially ineffable "converges into reality" riding the "root history" of this "word". I haven't quite worked out in my mind what I'm trying to say here.
On Tzvi, the Arabic word (more phonetically) is /.dh/b/y/ ظبي which is part of the name of Abu Dhabi (capital of the UAE). A Dhabi is somewhat a breed of Gazelles. Abu Dhabi's name comes from the historical fact that Abu Dhabi was the place that was populated by Dhabis.
I thought you would mention "keren hazvi" קרן הצבי - which Reuben Alcalay - The Complete Hebrew-English dictionary - translates as "dubious venture, doubtful".
Alex -
Steinsaltz points out that the land also shrinks economically when there are fewer inhabitants. An interesting point.
Toby -
Optimism is always good...It seems the Maharal says something similar.
Liorah -
Original as always.
Samawel -
I see there is also an Arabic "sabi" which is cognate to the Hebrew tzvi meaning "beauty". In Arabic it has the sense of "youth".
Zvi -
The idea here is that one "who puts his money on a deer's horn" is as one who cannot reclaim the unauthorized expense. Once you put your money on a deer's horn, it will be difficult to catch it again...
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