Below is the lyrics from the song "letter song"
I want to know what does ほど mean here? Does it mean "the more ... the more ..."?
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No, this ほど means "to the point where ～" or "enough to ～". It's this ほど, and is interchangeable with くらい/ぐらい.
I'm not yet old enough to stop or reflect on the meanings (of everything I come across) ...
Basically these lines are saying "I am too young to look back at what I have experienced".