Aeronautical/aerospace engineering is basically applied Newtonian mechanics. As a physics major, you most likely have quite a bit of coursework that is of limited applicability to aeronautical/aerospace engineering (i.e. quantum physics). I also suspect you are lacking in some areas critical to aeronautical/aerospace engineering, such as an advanced thermodynamics, guidance, navigation, and control theory, modal analyses.
The above was not intended to discourage you. I have an undergraduate physics degree and work as an aerospace engineer. A graduate student in aerospace engineering worked for my employer last summer, and his undergrad degree is in physics. He worked for me, in fact. So, it can be done.
I don't know about GRE scores of financial aid, but a 3.0/3.1 GPA is a bit too low for the top schools. The middle tier, which is what you talked about, are a good possibility. It will help if you have something going for you other than your GPA. Did you work on any undergraduate physics projects? Look to do that if you still can, and volunteer to be the lead. Do you have any outside interests, particularly anything that smacks of leadership roles? These extras will help you land a spot in a graduate program. They will also help you land a job later.