First, it is not a browser. You actually do commits, merges and manipulate branches.
The size is that big because Gitbox is bundled with official Git binaries so you don't have to install anything else. I will see how to bring the size down in the next versions. Anyway, this fact does not affect the performance and does not eat much memory.
git-osx-installer package takes 4.3MB, but your git.bundle takes 150MB.
The problem is that the bundle contains exactly same binary 104 times (git, git-add, git-apply, etc. are identical files, 1.3MB each). These should be symlinks.
It might be ZIP's fault (doesn't support symlinks AFAIK). I distribute my apps as tar.bz2, and nobody complained yet.
Gitbox is better because it is a pleasure to use. There are tons of little details which matter in a daily work. For instance, when you switch a branch and try to commit to it, the branch name will be highlighted to remind you that the branch was switched since last commit. If you forgot to switch back, you just cancel the prompt. This little thing instantly eliminates 50% of use cases for "git reset --hard" or "git cherry pick" and makes you happier.
Also, Gitbox fetches remote commits automatically so see that you have to pull something: this eliminates unnecessary merge commits.
Some of the applications on my computer that are bigger than Gitbox: Google Chrome, Wireshark, Inkscape, iPhoto, Komodo Edit, etc. My hard drive barely noticed when I downloaded Gitbox, so practically the only difference was a few extra seconds of download time that I didn't notice, that's all I was trying to say. Your comment was helpful to the developer in the end, so kudos.