Thanks for writing about this - I've felt this, too.
I have very porous boundaries, so it's easy to slip into someone elses moods/emotions at times.

I try to ask myself: Is this emotion/situation mine? And tell myself that I trust the other person to handle their own lives/find their own solutions, if they need my input/assistance, they'll ask for it. I think I can be more helpful if I can provide clear headed support rather than echoing their emotion back to them.

I seem to have sympathy confused with intimacy in my mind - what I mean is, by immersing myself in others emotions I feel I am closer to them, the relationship is stronger. I'm leaning that insisting on carrying other peoples emotional burdens isn't helpful to them or to me (not that this is what you or others are doing - just a reflection of my own tendencies).

I'll look forward to seeing how others deal with this. Thanks again for raising the question....