Enough about parents though, what does science have to say about this?
Multiple studies have been done on the subject. Not only is there no good reason to be concerned about negatively influencing your growth, there seem to be quite a few benefits to resistance training on a young age, just like it benefits adults. A wide variety of benefits have been observed: increase of muscle mass and strength, improvement of general motor performance, reduction of body fat and improvement of lung capacity.
The fear that resistance training will stop or slow down your growth is simply not supported by research, nor has it shown any other physiological downsides.
However, there’s also the psychological aspect to consider. While resistance training can improve willpower, general wellbeing and boost your confidence, you don’t want to develop any obsessions over your body when you’re young. When you’re seriously overweight, it’s safe to say your parents are too and you’re most likely not to blame. If you’re not, worrying about your image too much, in your pre-teen years, will likely result in a negative self-image when you’re older, so please consider that side of the coin.