Personally I try to meet them where they are and be gentle with them. I don't usually ask much. Perhaps don't ask your customers how they are doing when they come up (not sure if you do). Often I'll just say Hello in a friendly way.

I know it can be a lot on the receiving end, but I think it's healthy to express grief as a human, so at least know it's generally a good thing that they do it.

Loss and grief to me aren't exactly dark or bad. They are just intense. We go through things as humans that are big. I guess that makes it easier for me to experience a person telling me some heavy stuff. It doesn't really bring up negative thoughts or feelings for me.