This isn't anything against you at all, but I'm honestly having a difficult time understanding this. I suppose if I have a weakness it's having too much empathy for my own good. It even makes watching some movies very difficult for me, even though I can distinguish logically between a plot and true events in real life that have significant impacts on people.
Other folks answered this pretty well, but I'd also add that it depends a lot on the context, and there are times when taking a completely serious empathetic approach is less helpful.
If I mess something up at work, or put my foot in my mouth, or do something clumsy, or get drunk and do something embarrassing, or some minor catastrophe occurs to me, I'll talk about it with my friends, and we'll laugh about it. It's therapeutic, it turns the bad thing into something that spreads laughter and brings you closer to others, and it helps put into perspective that whatever the problem is, it's not some life-shattering event, but a stupid thing that's minor enough to laugh about. It usually also opens up a dialogue where others will talk about similar stuff that happened to them, and everyone pokes fun at each other's calamities. I'm laughing, but there's an unspoken supportive pat-on-the-back implied. It's a means of support, really, a way of saying "it's not as bad as you think" and maybe "I know how you feel", without actually being so unsubtle as to say it.
Because sometimes going full-on "oh God, I'm so sorry, is there anything I can do to help?" actually makes it worse. It's intense and it makes me more likely to think "oh crap, this really is a big deal, I really should be worrying about this".
Obviously, if we're talking about something major a bereavement or getting fired, then it's the opposite. And I wouldn't just start laughing at a complete stranger; there has to be at least some social pretext, for you to be able to read how the person in question is going to take it (OP invites us to laugh right in the topic title). But I'd say a ship crashing in a game fair game, while a car crash in real life wouldn't be.