This will be a quick one, stop saying “I’m sorry” unless you add in “I’m sorry for your loss”. However, that still isn’t a great way to speak to someone. The reason is simple, saying sorry is an implying of fault; you say sorry when you step on a toe because you did something to the other person. You say sorry when you cheated on someone and ripped their heart out of their chest. So, unless you have the cure to the ailment the person is suffering from but didn’t give it to them or you actually caused their death, don’t say “I’m sorry”. Instead, might I suggest you say “my condolences” as it is a far superior term. As someone who had to hear, “I’m sorry” about one hundred times in a single day, I find the phrase false and empty – but the fact that you were there to say it means more than anything else.
So, just show up and be present, share a memory and if you say “I’m sorry” that’s okay too (but you should choose a better phrase).