Praise be to Allah.
There is nothing wrong with using medicine to increase growth hormone for the one who is of weak build or noticeably short stature, because that comes under the heading of medical treatment and remedies. It has been proven that short stature is connected to a lack of growth hormone, and this is not regarded as changing the creation of Allah; rather it is treating a shortcoming and weakness so that the person may develop a regular appearance like that of his peers.
On Wikipedia it says: Growth hormone helps in building the human body (anabolism) by causing the bones and tissues to grow by means of increased protein production. In addition to that, growth hormone also contributes to breakdown of fats (lipolysis) and the formation of ketone bodies. This hormone also increases the levels of sodium, potassium and magnesium in the blood.
It also says: short stature is connected to a lack of growth hormone. Short stature may respond to treatment with hGH (human growth hormone) in the form of drugs. End quote.
Using this as a medical treatment depends on ascertaining that it is free of harmful effects, because the Prophet (blessings and peace of Allah be upon him) said: “There should be neither harming nor reciprocating harm.”
Narrated by Ahmad, 2865; Ibn Maajah, 2341; classed as saheeh by al-Albaani in Saheeh Ibn Maajah.
Hence it is essential to consult a specialized doctor.
For more information please see the answer to question no. 108860
And Allah knows best.