Having hiked lots of different parts of the AT, I can tell you, that you won't need anything more than a small sak or pocket knife.
The very fact that you're backpacking, you have weather proof shelter with you, as well as suitable clothing and gear for less than perfect weather. You won't be batoning any wood, simply because open fires are very stricly prohibited for most of the trail. If a park ranger finds you with an open fire in some areas, you will not just be given a summons, you will be arrested. espcially if there is drought conditions in mid summer. Because of the population of people using the trail in recent years, rules are taken extremly serious by the park service personel. The shelters have a fire ring, but you want to stay clear of the shelters as they are magnets for the vermin. Both four legged and two. They are infested with mice that will chew holes in your gear to get into your food while you sleep. The two legged vermin are the proffesional woods bums who disguise themselves as back packers, wait till you're sleeping, and steal your gear. I know one person who woke up and found his whole pack gone.
Once in the area of Wolf Mountain, my better half ran into a really shady charater on the trail with no gear, meaning he came from one of the small towns nearby, and he was pan handling right on the trail. He got a bit aggresive till I slipped a hand in my pocket and used some very vivid and strong lanuage on him. Too many parts of the trail are VERY close to depressed small towns, and the local yokals sometimes like to park thier pickups close, walk in, and hastle the hikers.
You're a young guy, and probably won't have a hastle, but keep your wits about you, and you can have a great trip. You'll be on the AT, not walking through Disney World. Keep that in mind. Not everyone you meet will be a nice peacefull hippy backpacker.
Select only the lightest and most esential gear.
Have fun.
As I got older, I had to cut my load, and I got tired of carrying a sheath knife that never left its sheath.
Be carefull on the trail from southern Virginia to mid Pennsilvania, alot of trail crime happens there. Robberies, a few killings, some rapes.
While I wouldn't bother carrying a sheath knife, I would certainly carry a small pocket pistol, and keep it totally concealed for the whole trip ON MY PERSON. Most trail crimes seem to be commiteed with a knife or blunt instrument, as in the case of Gary Hilton. He used an asp type of baton. It's quieter. Same for knife. Even a NAA .22 revolver will beat that. Aside from the girl on Blood Mountain in Ga., Hilton also killed an eldery couple in North Carolina for thier ATM cards. A small hide out handgun would have saved thier lives. Same for the couple in Virginia killed by Randall Smith.
Keep every once of weight down that you can from your pack. There are parts of the trail where you will be climbing up grades for a whole day, making your way uo a mountian.
STAY CLEAR OF THE SHELTERS!