If you say that your
heart bleeds for someone, you mean that you feel a lot of sympathy for them because they are suffering. Note: The heart is traditionally regarded as the centre of the emotions.
You looked so sad at the funeral and my heart bled for you. Note: This expression is often used ironically to show that you think someone does not deserve any sympathy, because you do not believe that they are genuinely suffering.
She's had to sell one of her three houses? My heart bleeds for her! I must say, my heart bleeds for the poor investors who made a mere 15 per cent on their investment in one day. Compare with
a bleeding heart.