Originally a song title by the punk band NoFX, Bleeding Heart Disease pokes fun at people who are "Bleeding Hearts" and "Heart Disease" (a real disease). Someone who has Bleeding Heart Disease often suffers from chronic and naive sympathy for anyone and everything, especially around politically sensitive issues. The sympathetic emotions are often unjustified and directed to people or causes that do not in fact deserve sympathy.
It's important to note that to be diagnosed with Bleeding Heart Disease, a person must chronically feel unjustifiably sorry for people on unrelated topics. It's also important that the topic of sympathy be unjustified or highly debatable.
Bleeding Heart Disease is becoming especially common in the Western World.
Statement: "That's so sad that guy died when he got his Darwin award."
Reply: "I think you have Bleeding Heart Disease."