"Wear your heart on your sleeve" means that you don't hide your
emotions. Everyone can see immediately how you feel about
something.
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You do this by outwardly showing your emotions.
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When he says "wear your heart on your sleeve" he's saying that
they would show their emotions more and not conceal their feelings.
When he says paper heart he's saying that their heart is very frail
like paper
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The old term is 'you wear your heart on your sleeve.' This simply means that when you are hurt by someone you care about that you do not hold back your feelings and that even by the look on your face your family and friends know your heart is aching.
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The term wearing your heart on your sleeve is thought to have
originated during Medieval Times. During jousting matches knights
would wear their ladies colors on their arm.