Had a similar problem with mine 2 years ago - would only tension up when I turned the ignition off ! Replaced the offending belt with a new one (well the main dealer did !) £125 ....and it still does the same 
Incidentally it's not just a question of phoning and ordering a seat belt - as I found out there are 11 different versions for the passenger side in my 600 and that's only in black ! Apparantly in the USA and Germany there are more 'stoutly built' gentlemen who require the extra length seat belts ! and of course various other lengths ! so you will need to quote your chassis number
Incidentally it's not just a question of phoning and ordering a seat belt - as I found out there are 11 different versions for the passenger side in my 600 and that's only in black ! Apparantly in the USA and Germany there are more 'stoutly built' gentlemen who require the extra length seat belts !
and of course various other lengths ! so you will need to quote your chassis number 
