If you can't land in PDL due to weather, you most likely will get delayed for a while in JFK. Since SATA has very few flights in general, this could be a few days. I've been delayed on a SATA flight leaving from Boston due to weather and stuck in Boston for 2 extra days (I don't live in Boston so for us that was an issue. If you live near JFK you might not mind). This airline isn't *great* with communication so you may not find out you won't fly until you've been waiting for a bit at the airport. Or you could have smooth sailing and everything is grand, you never know. There's no where to "divert" to really near the Azores (the islands are isolated). Potentially a plane could land on Terceira, which has the other large Island airport and is separated from PDL by a couple hundred miles, but I haven't experienced a switch like that. If the weather looks suitable prior to takeoff and turns worse, you might just have a very rocky landing into PDL. But then you will probably have a delay getting out....

If you're connecting flight can't leave PDL due to weather (or mechanical issue or something), yes, you could get stuck in Ponte Delgada for a time, even days. If you only have a few days off from work or that you can take this trip, without flexibility on either side, I wouldn't stop in the Azores. It's much easier to take off and land in NY and Lisbon than it is on the islands and you will just have a much much greater chance of delay in every direction by choosing the stopover. Wintertime weather in the Atlantic is harry... There isn't a ton of tourism to the islands during this time of year because it's not pretty and sunny, so they don't have as many flights available to bump you to.