The word 'sorry' is one that we tend to use far too often these days. It has become so common that it has lost its meaning. Additionally, when we use the word 'sorry' it has an impact on us. Let's look at how we use this word and how we can change to something else.
If a mistake is made, we automatically say "I'm sorry". By doing so we have owned the problem. But what if it wasn't you who made the error in the first place? In my opinion you should only say sorry if you have made the mistake. Say it immediately you make the mistake and say it with honesty.
If it is not your mistake, use the word 'apologise'. This word has greater impact on the listener and is a more formal acknowledgement of the error. Plus, we don't tend to absorb the issue personally as we would if we had used the word 'sorry'.
A common use of the word 'sorry' is when someone has told us a sad story such as "my partner has just died". Our first reaction is to usually say "I am so sorry for your loss". This is okay but are you genuinely sorry? If so, then keep using the word. However you could try saying "I can't imagine how hard this must be for you" or "That must be hard for you" or "In the circumstances let's see if I can make this easier for you". Anything that acknowledges their emotion and you aren't saying sorry.
Don't get me wrong, if using the word 'sorry' works for you then by all means keep doing so. Remember if you do that it may be impacting on your own emotions plus if you use it all of the time it will start to sound disingenuous.