I would think the most common criteria for "smallest" airport would be (a) airport physical size and (b) passenger statistics. Number of scheduled flights would also be reasonable, though it would probably correlate pretty closely to passenger statistics.

There are plenty that are smaller in both respects, but I believe my smallest three are Salem, Oregon; Elko, Nevada; and Ely, Nevada. Another possibility would be Johnston Island, back in the days when it was still served by the Island Hopper.

I am, of course, limiting the universe to airports with commercial passenger service!