Mortician here.

Deceased people actually do get "lighter". Immediately after death they loose 50-200 Gramm within seconds, mostly the air they had breath in and is slowly exhaled. After that they start to get lighter due to loss of fluids. I don't want to go into too much detail but it is not just vaporated water. Depending on position at death and temperature that can be around 10-200 Gramm per hour. That is for the trained eye quite visible as it mostly happens in the outer layers of the body. This also is the reason why deceased men often look unshaved, their hair doesn't grow, their skin just shrinks.

Most times it is very obvious if the person is dead. But I have also had some uncanny valley experiences where I thought "is she/he maybe just asleep?" In one case a doctor called me to an old woman where two police officers and the doctor claimed her to be dead. I arrived, we grabbed her to lift her up and suddenly she jumps up and scolds us for waking her up.

That was the first time when I had tea and cookies with a customer. She lived for another four years and died at age 101. I felt quite strange visiting the same person twice in my job.

Besides that, you get used to it. Keep it professional, slightly distant, developed a routine. The routine can and should include keeping respect at all time but not necessarily emotions. My Grandpa was pretty good at that, he could even shed a tear without actually feeling something. It helped the bereaved to open for their own emotions.