Wow, I didn't know people could just decide to leave the Army in the middle of basic. I thought once you were in basic, you'd signed on the dotted line and were committed unless you were dishonorably released or something. Guess I was wrong!
I did do some research and found that recruits who have been in the Army under 6 months can separate under an ELS (Entry Level Separation), which is neither honorable or dishonorable, but that usually takes more than a few weeks since it is usually granted only after every other effort has been made to increase the recruit's "compatibility" with military service.
Below, I've linked a page that seems to describe well what I found on other sites:
http://armybasic.homestead.com/leaving.html
Of course, you can feel free to hang around if you'd like, but if you don't, I hope everything works out well for you, Zenycha.
Love 
