Hey, yes I have been thinking a lot about this topic too.
I have a tendency to be very accommodating with others and constantly worried that I might hurt/offend others and therefore I apologize a lot.

An old colleague of mine used to tell me that I should stop apologizing for everything, or else people will step all over me. He was right, at least in part.
This tendency to always be extremely careful with how I interact with others does indeed make me anxious, as I have to plan what I say or do with others a lot. All too often, some others will just be quicker than me at talking or making decisions and I will find myself just being passive or left behind even when I deeply disagree with the principles behind the decision. I think I often even give up thinking of what I want in order not to be disappointed later.
I even have had several situations where people with narcissistic traits have taken my tendency to apologize as a tool to blame me for everything, including their problems, to the extent that they would blame me of deliberately hurting them (me??????????? yet I believed it lol). These situations are really hard for me to deal with.

I also often find myself listening FOR HOURS to completely random people who decide I should listen to all their problems and do not seem to care how I feel or whether I have something to do. Like, really random people: the guy I'm renting a car from, the bank employee, the neighbour, the person sitting next to me in a plane etc. In this kind of situations I start by truly caring and wanting to listen until I realize I do not know these people and I would much rather have more time for myself. But, because of lack of assertiveness, by then I am normally "trapped" and will have to listen to the full story.

On the other hand my ability to empathize (and at times overempathize) does strengthen good relationships with some people. Few but good. Both personal and work relationships. I also think I do not want to give this up, I still think that caring is a good thing and that I really would like a world where more people care.

Being able to set a limit sometimes would be good though. Basically, we need to remember that a) just because someone is blaming us, it doesn't always mean that it is our fault b) sometimes we just have to put our own needs first. The trouble is, remembering that we have such needs and that they really are necessary for us to feel good. Feeling good is not a luxury, it is something we have the right to defend.