I was in the USAF (for three months!) and in Basic, it seems the ONLY thing they care about is honesty during the initial recruitment process. For instance, if you admit to prior marijuana use at the time of enlistment, they will likely allow you in... BUT... let's say you DO NOT disclose it; after you arrive at training, you will be told that "you have one more chance to tell us anything you may have lied about when you enlisted," and this includes marijuana use. While I was there, everyone who admitted to marijuana use, suicide attempts, illegitimate children, etc was sent home almost immediately. I was sent home after injuring my ankle on the track. Six mile daily runs really put your body through some serious $h!t!
Whether they will let you ship off depends on a variety of factors; ASVAB scores, criminal record, overall health, etc... since the NAVY is at (or near) capacity (and the war is "over,") they're being even more scrupulous. Your best bet is to lawyer up, get this mess behind you, and get to Chicago ASAP (before another jerk cop decides to ruin your life).