勉強すればする程、日本語が上手くなる。
If [you] study, [your] Japanese gets good to the extent that [you] study.
God, this makes so much more sense now! At first I tried to translate it as
If you study, your Japanese gets so good that you study. (What?)
Meaning that first your Japanese gets good and, as a consequence of that, you study.
I think at first I got the wrong idea that the part preceding ほど is always the result/consequence of something. As in:
死ぬほど練習した。
I practiced myself to death.
(I 練習する and, as a consequence of that, I 死ぬ)
涙が出るほど嬉しい。
I am so happy that I could cry.
(I am 嬉しい and, as a consequence of that, I 涙が出る)
But here it’s the other way around: first you study to some extent and, as a consequence of that, your Japanese gets better.