Breed is not a significant factor regarding when a horse will stop growing. All or most horse's bones will stop growing at age 5-6, so your horse will not grow any taller after that (although he will 'fill out' with age and training for the rest of his life). However, most of the height growth is done by 3-4 so I doubt he is going to get much taller. I would say his adult height is going to be a generous 15.3, but it would help to know the exact heights of the sire and dam. Also, height isn't everything when it comes to jumping. There are many famous jumping horses who are in the 15 hand range that could jump much higher than a typical 16.3 horse.
"The trouble with the world is that the stupid are certain and the intelligent are full of doubt"