Hi, My name is Tony and live on Staten Island, NY.  Here's my questions:

• This is the first year since Sandy that my fig trees are producing figs.  The problem is that they are unusually small.  What can be causing this?
• Each year since Sandy, my fig trees have to be cut down to the base due to winter damage.  The fig trees are old and I don't cover them any more.  They are now a large bush structure with many branches.

 fruits is small due to insufficient water/fertilizer/sunshine issue, or there are too many fruits in a small tree.
1st year fruit doesn't represent the quality of the variety, you need to wait for a couple of years to get stable outcome.

my guess it is having die back because all the new growth is not old enough to handle the cold. The branches etc do not have enough mass and moisture to counter the dehydrating effect of winter cold.
I would try giving the new growth winter protection for a few years.

From what I noticed in my figs in pot, heavy pruning does decrease productivity the first year on certain varieties and could even totally eliminate the crop for that season.
Most of the energy goes into the new growth. In your case I suspect that the same thing is happening. Try to protect your tree in winter and see what happens.
Make sure that there's enough nutrition in the soil by fertilizing on schedule. When fertilizing, you might not get immediate results. It might take a full season or longer before the tree reacts.

Hi Tony. I'm in SI too. My fig tree that is about 15 years old didn't do well with the two harsh winters we had. I cut it back and all new growth came from the bottom. This year it is producing figs (I had no figs on it last two years.)They seem to be ripening much later. Yours could be smaller since they are just coming back from Sandy. Maybe the soil lost some nutrients. Good luck!