I must have a penchant for remote areas, because I've been to quite a few airports on this list!
Smallest with commercial service though would be Edward Bodden Airfield in Little Cayman - no security and no more than a shoebox of a waiting area.
For a US airport, I'd offer Palomar Airport in Carlsbad as getting jet service but boy is the passenger terminal area small. For the baggage claim the rampers just dump the bags from the trucks onto an outdoor ramp.

I have flown into/out of both airports and they both qualify as very, very small commercial airports. Which reminds of West Yellowstone Airport (WYS), which by these standards is just very small, but not very, very small. But the “baggage claim” is a bench at the curb. These days, I think WYS has 4 commercial jet flights a day in the summer (2 DL and 2 UA).