My sister has no empathy. I'm going through a lot of health stuff at the moment and she sent me a robotic text asking how it's going and that our mother told her what's going on. No good wishes, or any sort of normal engagement from a sibling. I responded in a bland sort of way and she didn't respond back. It doesn't matter to me, I went low contact years ago because being in a relationship with her is very hard.
My dad is so empathetic he can't function - he shuts himself down as a defence mechanism and is basically a hermit. It makes him seem very self-centred and unempathetic when the opposite is true. I've inherited the same trait - I feel other people's feelings very acutely and it is torture at times, though I am able to manage it most of the time. I can generally predict people's reactions and behaviours much better than other people can, largely because I can understand their thought processes. It makes me very understanding but at the same time it is hard not to get overly concerned with everyone else's feelings and neglect my own.
My mother has proto-empathy - empathy on the level of an 8/9 year old child, where she can sort of understand how another person feels but she can't process it at all and she has very immature reactions to things. At 70 she has developed some level of skill but it is still nowhere near what you'd expect from a typical adult.
You can imagine my family is an interesting bunch!
Empathy is a funny thing - I was telling a friend yesterday about a situation I'd gone through earlier in the year with a child she didn't know - the child was very sad and scared - and she got tears in her eyes. She has no connection whatsoever to the child, yet she was able to imagine and feel how he was feeling. It's quite hard to live like that - both she and I have defence mechanisms because in a world where so many things go wrong it's like living with raw nerve endings. That said, I feel joy very acutely too and absolutely revel in the happiness of others, so it does have a great upside!