I don't know about the costs of the growth hormone treatments. I assume insurance covered a lot of it. I'm not sure exactly how they determined I had a growth hormone deficiency. It started with the fact that I wasn't growing much for a long while and was a lot shorter than I should be even given my parents' heights. My doctor had my parents take me to a specialist. A bunch of tests were done to rule out any other possibility than a hormone deficiency. If you want more details, I could ask my parents. I was a kid at the time after all.
There are several reasons I want to be taller, at least some of which I wouldn't talk about with my family. For example, I'm attracted to tall women, and I think being taller would allow me to attract tall women more easily. That is by far not the only reason. Another reason is that the 6 foot mark seems to be the mark that says a man is tall. Tall people make more money. Also, for many years I have wanted to be really tall. I was bullied a lot when I was a short kid, and that just increased my desire to be tall. At the time the bullies just seemed so tall. Even though I have grown, my desire to be tall has not subsided. I know that I have outgrown several of the people who bullied me for being small, but I would like to be even more taller than them. I also have a lot of friends who are taller than 6', and I would like to their height or closer to their height.
