Why is the word "sorry" used for this dual purpose? It seems to me they really have nothing to do with each other at all. Is it purely coincidence, like the dual meaning of "bore"? I find this unlikely. Is this present in (and derivative from) other languages as well?
To clarify, why is sorry used for these very different sentences?
I'm sorry that I stole your bike.
I'm sorry to hear that your bike got stolen.
"Sorry" was originally a more general word for sadness or misery. You don't hear it used this way very much anymore, but its use in apology and sympathy both stem from that original sense. As an apology, it's essentially short for "I'm sad that I did this thing." As an expression of sympathy, it's short for "I'm sad for you, as you go through this situation."
The word stems from 'sorrow'. 'Sorrow' is present in each of the two examples. I feel sorrow for having stolen your bike. I also feel sorrow if someone else stole it. It does makes a nonsense of the modern fashion for demanding that governments apologise for things; Americans for slavery, British for the Highland Clearances etc.
'Sorrow' is not something which can be required by the injured party. It cannot be an elective principle. It has to be something which sincerely arises without prompting. So perhaps it is true to say that the term 'apologise' has come to mean something different to an expression of sorrow - which is why we say 'sorry'.
