Welcome to the board! I think that it's great that you and your son want to do this together.
I work in San Antonio and live nearby; Big Bend is perfectly safe, at least with regard to the type of incidents that you're likely concerned about. I regularly visit http://www.bigbendchat.com
and can't recall any reports of problems. In fact, the community is very excited that they're about to reopen the border crossing at Boquillas. http://www.gpo.gov/fdsys/pkg/FR-2011-10-28/html/2011-27792.htm
Anyone planning a trip to Big Bend can find a wealth of information and lots of very experienced, helpful and friendly folks at bigbendchat.com. I recommend heading to the Chisos Mtns for your first visit to the park. It's well away from the border and has amenities (lodge, restaurant, store) if you feel that you need them. Here's a trip report with links to pictures from my last visit. http://www.bigbendchat.com/portal/forum/your-trip-reports/chisos-mtns-930-102/msg110947/#msg110947
I don't want to hijack your thread so I'll shut up about Big Bend and get back to your original question now. Your original question asked "how much weight" so I realize that this isn't a very good answer from that viewpoint. At 110 lbs, your gear needs to be as light as possible. We live in a semi-arid area with limited water resources so there will be times when you'll carry as much water weight as gear.
I don't know how much gear you already have but with Christmas approaching, I feel compelled to say this. Many people don't fully appreciate the difference between backpacking and "camping with a backpack" and will, with the best of intentions, buy you stuff from Cabelas, Bass Pro, Dicks or Academy that you can't use because it's too heavy or otherwise inappropriate. Gently encourage them towards gift certificates and wait a bit before cashing them in, for you will find that your idea of suitable gear will change too as you learn more.