It's true that weight training could stunt your growth, but only in extreme cases.
Weight training is commonly known to strengthen your body all the way down to the bones. GPs are very often prescribing older people to go to the gym and use weights to help prevent the onset of osteoperosis.
It's claimed that it helps strengthen joints, encourages good posture (which as we all know leads to better bones and muscles as we get older and even proper use of the lungs, so they stay strong til an old age), adapts hand-eye co-ordination when faced with opposing forces, trains the individual a sense of discipline both physically and mentally (if they abuse their technique in the gym, even with the light weights they can damange themselves) - it has so many benefits!
Schools around my way have (i think) 2 sessions a week where the kids can go to the local gym and work out.
It's encouraged for most ages, but to certain extents. Heavy lifting, however, is strongly discouraged for anyone still growing, or too old and of course for someone who's unaccustomed to heavy lifting. There's a very small bracket of people that can endure heavy lifting and it takes time, patience and knowledge before you can start safely pushing your body through - what you originally thought were - it's limits.
Bulking up at 14 is not the way to go about it, but avoiding weight lifting simply because you're still growing - that is most definitely a myth.