Something is going wrong with the rear seat belts. The lights illuminate when you turn the key but then go off. I do not think they make any beep if somebody is there with no belt but I can be wrong.
The front passenger seat has a weight sensor and it beeps, e.g. you could have a bag there and when you hit something on the road, it can activate the beep. Maybe the back seat has some similar function but I am not sure about that. In the manual it only mentions that the front seats have it.
Try to buckle the back seats and find out whether there is something stack in there. Something must close the cicrcuit for the warning lights. Maybe something has been cut within this circuit. Somebody else has mentioned that there is a tube which closes the circuit when you buckle the belt but I did not understand what he was referring to. He says that this tube was cut in this bar and he separated the two so that they did not touch and make contact.
Lastly, there may be no problem with the belts at all but the unit that illuminate the warnings is not on continuous contact. I had an airbag light on because the bulb of the warning had come off place and was not making contact. As a result, the circuit could not close. But that small device above the rear view mirror, seems like a sealed unit.
I am pretty sure you could try to take it apart but before you do that, do the belts properly and then notice any difference. Also drive the car with the belts buckled. If you have bought the car from a franchice dealer, you could go back and ask them to fix it.