grammar - What is the うち in 使っていくうちに?

The following excerpt is taken from a conversation with my language partner:

「てform の使{つか}い方{かた}」* を読{よ}みました。このように書{か}いてあると、難{むずか}しく感{かん}じますね。
私{わたし}たちが「てform」を使うとき、「この動詞{どうし}は意志{いし}を表{あらわ}すから」などとは考{かんが}えません。

子{こ}どもの頃{ころ}から使っていくうちに、身{み}についてきたものだからです。でも、日本語学習者{にほんごがくしゅうしゃ}にとっては、分類{ぶんるい}してある方が、わかりやすいのでしょう。

The sentence in question:

子どもの頃から使っていくうちに、身についてきたものだからです。

My attempt at translation:

"From when one is a child, ..."

I must admit that I really can't make any sense of this sentence. I guess that she's trying to tell me that they are using it from childhood on and that "it just comes by itself" (the proper use of て-form), but I don't know. I can't even tell the morphemes apart; is it "いくうちに" or "いく + うちに"?

And what about 身について? Is it 身 + について?

Maybe

身についてきたものだからです　=> "regarding oneself, because it is a thing that came."
or "because it is a thing which came to oneself."

where I regard について as に+ついて, with ついて being て-form of 着く. I always feel a bit uncertain about my understanding of this.

As I use it, it often resembles the use of は as a topic marker, translated to "Concerning X". But from a grammatical perspective I think that the two are quite different.

*(see here for the article she is referring to https://www.learn-japanese-adventure.com/te-form-cause-reason.html )

Answer

From Jisho.org. Second definition of うち reads:

2. while​

Usually written using kana alone, See also ないうちに, also 裡

あの[少年]{しょうねん}は[店]{みせ}から店を[歩]{ある}いているうちに[盗]{ぬす}み[癖]{ぐせ}がでてしまった。
The young boy got sticky fingers when he walked into stores.

First definition of 身につく is:

1. to master (e.g. a skill); to become accustomed to (e.g. a lifestyle); to acquire (e.g. a habit)​.

This also uses the 〜ていく grammatical form.

My rough translation for the passage in question would be (feel free to correct me):

The て form is something we master after using it again and again from childhood.

The other things to be mindful of are the 〜てくる and ~ものだから grammatical points.