There are 2 types of tags - lightweight and annotated. Lightweight tags are merely refs that point to some object whereas annotated tags are a separate git object by themselves, and store a lot more information like author, committer, a commit message, etc.
When you used git tag -a to create a tag, git would have created an annotated tag for you.
The ^{} is the syntax used to dereference a tag. It is described in gitrevisions.
When used with tag objects, git would recursively dereference the tag until it finds a non-tag object.
When used with non-tag objects, it doesn't do anything and is equivalent to skipping the ^{}
The refs/tags/v0.1.6 ref in your repository points to the tag object bb944682f7f65272137de74ed18605e49257356c, which in turn points to 771a930dc0ba86769d6862bc4dc100acc50170fa (a non-tag object) which I'm guesssing is storing the commit information when you created the tag.
So when you do refs/tags/v0.1.6^{}, git is going to dereference the tag and resolve it to 771a930dc0ba86769d6862bc4dc100acc50170fa - the non-tag object.
There is also a git show-ref command that can be used to list only tags, and optionally dereference as follows, and in your case should produce the following output:
$ git show-ref --tags
bb944682f7f65272137de74ed18605e49257356c refs/tags/v0.1.6
a72251d945353a360087eb78ee75287c38a1c0e6 refs/tags/v0.1.7
$ git show-ref --tags --dereference
bb944682f7f65272137de74ed18605e49257356c refs/tags/v0.1.6
771a930dc0ba86769d6862bc4dc100acc50170fa refs/tags/v0.1.6^{}
a72251d945353a360087eb78ee75287c38a1c0e6 refs/tags/v0.1.7
d69e66d7c915b9682618b7f304b80cc0ae4c7809 refs/tags/v0.1.7^{}
To confirm this, you can use git show command to give you more details about the git object.
This is the information from one of my test git repositories.
$ git show 43f9a98886ba873c0468c608f24c408b9991414f
tag v0.1
Tagger: Ash <tuxdude@OptimusPrime>
Date: Sun Jul 15 00:14:43 2012 -0700
Tagging Stable repo 0.1 :)
-----BEGIN PGP SIGNATURE-----
<PGP-SIGNATURE>
-----END PGP SIGNATURE-----
commit e55df25f2321a6b2c9a02fa80ccba7cbe3c38c08
Merge: 796efcd 58e3a4d
Author: Ash <tuxdude@OptimusPrime>
Date: Sun Jul 15 00:02:44 2012 -0700
Merge branch 'dev' into 'master' for stable 0.1.
$ git show e55df25f2321a6b2c9a02fa80ccba7cbe3c38c08
commit e55df25f2321a6b2c9a02fa80ccba7cbe3c38c08
Merge: 796efcd 58e3a4d
Author: Ash <tuxdude@OptimusPrime>
Date: Sun Jul 15 00:02:44 2012 -0700
Merge branch 'dev' into 'master' for stable 0.1.
