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This means, everything you say is being thought over and absorbed by ther person reading or listening

if someone were to say, i'm hanging on your every word
it probablly means that they can't wait to hear what you are going to say and are basically looking for some possible other meaning to what you might have said.
Why is it taking you so long to write back?

I'm hanging on your every word
by AriBea September 11, 2006