Does the granite countertop on my deck require separate footings?
Assuming your deck is somewhat modern and properly designed and built, it can easily handle a live load of 13 pounds per square foot (no extra footings required, no need to worry about aligning the table legs over joists, etc).

That said, I am assuming your deck is somewhat modern and properly built.
You should consider paying a structural engineer to take a look at your deck (especially the ledger connection to the house, which is a typical weak spot).  That would be a lot cheaper than pouring new footings and going crazy overbuilding it, plus it will give you a piece of mind.  You might be surprised how inexpensive a structural engineer costs to take a look at your deck and give an opinion.