If the room amounts to an addition to the house, you are going to need a building permit and the construction will have to meet code. 16' with
2x6's is way too big a span even for a deck, unless there is a beam down the middle--is there? I'm visualizing your doubled 2x10's as the rim of the deck.But if there's a beam down the middle, then you should be ok as things are. An 8 foot span is pretty much the limit for 2x6's. If no beam, then even
2x10's is not really enough, you would need 2x12's.