I'd sooner say "a heavy loss" (pesante) if the survivors continued to suffer after the person's death. "A great loss" indicates the value and esteem of the departed. "A big loss" sounds tactless in regards to a person's death.

I'd explain in such way - a heavy loss for close people, a great loss for humanity, a big loss usually use in business(

You would express your sympathy by saying, "I am sorry for your sad loss. Please accept my sincere sympathy."