can be think as blow-word -> blowing words -> means talkative
blowhard - like we say in hindi fekta hai saala :) or fek(blow) raha hai
blow + hard -- imagine someone who blows words in a way as if he is blowing air -- too many words, hence talkative.
(blow)ing his own trumpet (hard). One who boasts himself.
imagine a person blowing(boasting) that he is hard but instead he is weak..
from the proverb - one who blows his own trumpet