We carry a bag and biohaz kit.
These situations are always complicated, and there are no hard-and-fast rules that I can offer. It's tough on everybody when somebody dies and as each scenario tends to be distinct, it is not possible to provide specific guidance.
Fo the OP - factors to be taken into consideration for a turn-back would include the need to burn off/dump fuel to reach a safe landing weight, flight crew hours restrictions and hotel availability should (as would be likely) a night-stop back at the originating station be required: If at home base, a new crew would need to be sourced. Set against that would be the inconvenience and distress caused to other customers as well as the legals.
The most common practise when a Death-On-Board occurs would be to cover the deceased with a blanket, place an oxygen mask over their nose/mouth and make as "comfortable" as possible (yes, I know): The intention being that casual onlookers will be unable to tell for sure that the person is deceased as opposed to being unwell. This is not always possible since not everybody who dies does so in their seat - It can often be in or outside the toilet area. I have heard of bodies being placed or left in toilets and this cannot be ideal: Distressed relatives would hardly be expected to approve. Once again, you have to make it up as you go along to a large degree.
It is possible that apart from those customers in the immediate area, relatively few others were aware of the situation if the body was at the very front of the aircraft. It's not really good form to drag The Departed around the cabin to the cheap seats.