Warning! Armchair psychology here:
Could you be overcompensating for something?
Someone or some incident in your early life or childood made you believe you are a bad or selfish person?
It must be exhausting for you. Or do you feel better after crying?
Does it get worse when you are stressed out or going through difficult times?
Might CBT help? For example, how offended they would be if they knew how much you pity them? Or if their lives are actually much better than you expect or even yours? If they disliked you or thought what you are doing is weird? If they are in reality abusive, fraudsters, nasty ...etc? Would any of this jolt you back and make you reel in your emotions?
I don't think this is an issue of empathy, necessarily.
Do you then have people comforting you, making a foss of you or even complimrnting your kind heart thus giving you attention? Peehaps its a sign to others not to upset you because you are a good and sensitive person?
Is it that you feel you can't cry for yourself and own sadness and disappointments but find it easier to explain and less indulgent to release your emotions under the subtext of it being about others?
I'm fascinated by this becauae my mother was like you.