Is the airbag light supposed to show off on passanger side when proper weight is seat vehicle starting 2005 durango?

No, the passenger-side airbag light should not be illuminated in a 2005 Dodge Durango if the passenger seat is occupied by someone of sufficient weight. The light indicates a problem with the passenger-side airbag system. This could be due to a faulty sensor, a wiring issue, or a problem with the airbag module itself. A properly functioning system will only illuminate the light if there's a malfunction or if the passenger is too light to trigger the airbag deployment.