Having furniture in the rooms will not materially change your utility bill. Sure, the weight takes longer to heat or cool - then again, it takes longer to heat or cool. It means longer run times, but also longer rest times.
Closing off the rooms or their vents isn't a great plan, either. Your HVAC is sized for your entire house, not just a portion of it. If you close off the rooms then you subject the rest of the house to short cycles, which can lead to a chilly yet muggy house, as the unit doesn't run long enough to perform decent dehumidification. Worse than that, it can lead to mold and mildew formation in the closed off rooms if their air isn't circulated and dried appropriately.
NOTE: if you have a multi-stage or variable-speed HVAC system, then the aforementioned doesn't apply. Close off rooms if you want.