I've been looking to gain muscle/lift a little in order to be less weak.
Unfortunately, I only own one pair of 10lb dumbbells which I use for dumbbell pressing. As a weak 6'0(182cm) 132 lb.(60kg) 17yr old, I don't have access to public gyms, or buying more weights.
My question is this:
Will increasing the number of reps I can do back to back help with muscle gain, or will this gain plateau eventually?
If so, are heavier weights absolutely necessary for muscle gain?
Yes. Muscle growth requires progressive overload, among other things. Maximum hypertrophy occurs in the 10-20 rep range, and to continue growth it is important to ensure that exercises in the range remain difficult - which generally means adding weight as exercise becomes less stressful.
Once you can easily do 20+ reps with your weights (which won't take long for any exercise) you are longer training for hypertrophy, but muscular endurance - essentially, training for the ability to perform work for long periods of while flushing lactates from the area.
While it may be possible to achieve some growth with 10lb weights and bodyweight exercises you will plateau quite quickly. So, if you are aiming for muscle gain you are going to need to look at lifting more weight.
Weightlifting on a budget
In a pinch, if you can't get to a gym, get a cheap but solid calico bag, and make some smaller approximately weighted bags of rocks or sand. You can make a good workout bag, and then add or subtract weight to change the difficulty as required. If you can get enough rocks and a big enough bag, you can put on some muscle mass, but even then you will reach a point where adding more weight to a bag become unwieldy. The question becomes, are you happy with where that plateau point is?
I really like the question as its something that a lot of teenagers struggle with at this age.
To your question "Will increasing the number of reps I can do back to back help with muscle gain, or will this gain plateau eventually?" the answer is Yes you will gain a drop of muscle but not alot, and Yes doing the same thing all the time will cause you to gain a plateau.
Having said that I think you need to look at other options ifd you are serious about getting in better shape, the best option for you would be is to look to get a program, and I will list 2.
would be to get something like INSANITY or T25 if you are looking for something less intense, and thew are both from Shaun T, the benefits of these programs are, one that they do not use any weights, just a band occasionally, and 2nd and most importantly using a program will help you better keep track of your progress and make sure that you don't hit a plateau, but again you mentioned that Buying weights is not an option and if its because of financial reasons this would probably not be an option as well.
would be to follow a guy who I have followed his name is Matt Furey, it will be very cheap and it will help you gain overall strength, some muscle as well.
Here is a link to his website http://www.mattfurey.com/index.htm
You can also read the following to get more insight http://www.bodybuilding.com/fun/mahler19.htm
Routine #1: Killer 200 Pushup Workout: 3 minute back bridge 100 Hindu Squats 50 Hindu Pushups German 50: 10 Elbows in, 10 hand over hand, 10 Superman, 10 hands wide, 10 hands backwards performed in a row, without stopping. 25 Hindu Pushups with feet 10" apart 25 Hindu Pushups with feet together 25 Hindu Pushups with hands and feet together 25 fingertip Hindu Pushups 3 minute back bridge, 3 minute front bridge.
Routine #2: 3 Minute Back Bridge 100 Hindu Squats 10 Grasshoppers 35 Bootstrappers 10 Kneeling Back Bends 20 Hindu Jumper Squats 10 Mountain Climbers.
This is officially a beginners routine, but for most this will be too much, so do the sets as listed but with less reps.
I hope all this helps you, I will list a few tips that will help you along.
I don't have your lean factor but from the info you provided i would say that your calorie intake should be at least 2000 calories a day not less.
Don't rush into anything as it will do you more harm then good, try to find someone who has done these programs and get more insight as to if the intensity level it will suit you.
You also have the 132 lbs. of your body available to you although it is easier to use it to exercise some muscles (e.g., chest and triceps via push ups) than others. Given that you are a beginner, you can start with a program that uses body weight plus the small weights you have. By the time you max that resource out, other options could become available or you can jury rig something like @Stormtroopr suggested.
Ten pound dumbbells are close to useless for building muscle. You are a young man, in the prime age for lifting and growing. Find a way to acquire weights. Used weights on Craigslist would be best, since lifting heavy weights is the best and fastest way to gain muscle and strength. Look for a barbell and squat rack, or failing that, for 25 and 50 pound dumbbells.
It's possible to get stronger without heavy weights, but it's harder and much slower and often doesn't result in getting bigger. I highly recommend barbells or dumbbells. If you absolutely can't or won't find equipment, then look into bodyweight training.
