ZSU Controller described a altitude and course deviation by an enroute aircraft apparently because of severe turbulence; the reporter indicating expanded range weather equipment was needed.

Narrative

Air Carrier X called approaching ANADA intersection; northbound; and was deviating west for weather. My D-side coordinated with TTPP Center and I noticed that he made nearly a 70 degree turn to avoid [weather] and requested more. I inquired how much more; because of adjacent airspace; then approved it. My D-side called the adjacent sector; SVMI Center; and told them about the deviation. Air Carrier X was heading southwest bound into SVMI's airspace; so I changed communications over to SVMI Center. At that instance the pilot stepped on me and I caught the end of the transmission; which I heard; 'descending to FL330.' I could hear the urgency in the pilot's voice and asked him to clarify and advise if I could provide any assistance. I assumed it was turbulence and waited a moment to allow them to regain control. I then ask for conformation about the descent; if they wanted to declare an emergency; and if they had injuries or structural damage. All was negative and severe turbulence was the cause. They slowly proceeded back on course and climbed back to FL340. The area of severe turbulence was too far out of range for any accurate weather information from our NEXRAD. I was only painting small scattered patches of moderate weather. In addition; I had no previous reports of moderate or severe turbulence. I notified the FLM as soon as the pilot started descending. Recommendation; better long range weather RADAR.