How much time does one need between a flight from st Barts and a flight to New York out of St. Martin? Is it a big airport?

It's not a big airport. Personally, I would allow at least an hour 1/2. It all depends how many airlines are landing at the same time. The line through customs may be long (took me 30 minutes last month). Then you have to get your bag. Then you have to go check in for your flight to NY. Then you have to go through security to get to your gate.

the official requirement for check in is 2 hours ahead of time, so I would allow at least those 2 hours to transfer and check in

The big problem is the airport in St. Barth, and what you might call the "phantom" scheduling of flights. Recently it has not been uncommon for a "reservation" for, a particular flight to result in a heart-pounding sprint to the SXM gate, and even missing the flight-- why? because the flight doesn't exist. Planes seemingly come and go on whim, especially during slower seasons. I have had reservations for flights that left SBH two hours late, or even an hour EARLY. My advice? First of all: you will be MUCH HAPPIER if you are not checking bags. Carry On is the way to go. Book a flight three hours before your scheduled flight to NY. Go to the SBH airport first thing in the morning, check in and ask how things are looking. Try to ascertain the conditions that day. Then, depending on the situation, you can wander around the area, being alert to the flight realities. Keep in mind that the puddle-jumpers don't have any responsibility for your making your connections.

We've run into some major hassles at Juliana Airport in the past, so we always allow at least 2 - 2.5 hours at the airport. It's a big gateway to Miami for connections and there's almost always a long line. If check-in is a breeze, we go across the street for a good burger before boarding our flight.

Surprisingly, we've had pretty good luck in SBH for getting onto our scheduled flights. I second elisemf's recommendation for carry on only. Makes it easier all around, coming and going.