Driving screws back into weathered deck
From what you are describing you are using the wrong drill bit or not applying sufficient pressure.

Make sure you have the right # drill bit for the screws. The wrong bit will strip the heads making it difficult to extract or to drive the screws further in.

If you are using the right drill bit, stand directly over the screw and apply sufficient pressure when drilling. 

I would find it hard to believe that all the heads are stripped, but if the majority are stripped, my advise would be to get a screw extractor and remove the troublesome screws.  

Work with a friend or family member, 1 with a drill bit, the other with the extractor, systematically go down the deck and you'll be done in no time.