At 16 years old I was 4'11 17 years old 5'10 now still 5'10. Growth is stopped for most at 20, though I haven known repressed growth to occur as late as 22.
Sudden burst growth like mine is usually the result of repressed growth and this is generally through stress/ depression. Most in puberty just grow when testosterone is at a height, I have had to learn all about this to be able to teach it to my home educated son.
Lifting weights is very unlikely to stunt your growth if you are sensible, rep ranges 10 at minimum and PRE (perceive rate of exertion) at 8/10 maximum. So even if you can lift 200kg on deadlift for 1 rep, don't lift the weight you could lift for around 15 reps for 10 to 12.
This is nothing to do with puberty, in fact the increased testosterone in your body will mean you will gain more muscle from this lower intensity training than I would comparatively. Comparison is difficult because I am not growing anymore or developing internally. The reason you shouldn't do more intense stuff than this is due to your bones not having fully grown and fused. Much as it sucks until that has happened it is not advisable to do maximum lifts. We are discovering more all of the time but at this point we don't have enough evidence to make this claim invalid. We do know weight training is safe for virtually anyone if managed well so do go ahead and pump some iron.
Check out Goldfish's sticky in young athlete development. It's a very good generic start point.