All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is nothing wrong with exercising for the purpose of increasing one’s height, if we assume that this is possible. Exercise (sport) is a reason for strengthening the muscles and making them bigger, and decreases the weight: neither this nor that is considered as changing the creation of Allah.
If one exercises and practices sport and his height increased, then this is not changing the creation of Allah that is dispraised in the Sharee’ah.
It is Allah who increased his height because of a permissible reason, which is exercise; it is like treating one’s slimness with lawful food; this is not the changing of Allah’s creation because of the intervention of a human being and his surgical intervention, for example.
The greatest concern of a Muslim should be improving his conduct and perfecting his acts of worship.
Ibn Mas’ood narrated that the Prophet used to say: “O Allah! You have made my creation perfect, so make my moral characteristics also be the best.” [Ahmad] [Its chain of transmission is classified by Al Arna'oot as Hasan]
Allah knows best.