PREMIER 1 PLT ON DEP FROM TEB ENCOUNTERS SEVERE TURB AND CLBS ABOVE ALT RESTR.

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I WAS DEPARTING TEB RWY 24 AND GIVEN AN IFR CLRNC INCLUDING THE TEB 5 DEP (RADAR VECTOR). THE DEP CALLS FOR AN INITIAL CLB ON RWY HDG TO 1500 FT BEFORE TURNING WBOUND. ATIS AT THE TIME WAS RPTING GUSTY WINDS FROM THE SSW AND LLWS ADVISORIES WERE IN EFFECT. IMMEDIATELY AFTER TKOF MY ACFT EXPERIENCED SEVERE TURB. WHILE TRYING TO LEVEL OFF AT THE REQUIRED 1500 FT MSL; MY ACFT HIT AN AREA OF TURB AND MY ALT ROSE TO 1800 FT. THE CTLR SAID I WAS NOT SUPPOSED TO BE AT 2000 FT (I SUPPOSED THE ALT HIS RADAR SHOWED) AND I SAID THAT I UNDERSTOOD THAT AND WAS EXPERIENCING SEVERE TURB AND 'DOING THE BEST I COULD' TO MAINTAIN THE REQUIRED ALT. I DID NOT RECEIVE ANY TCASII ALERTS OR RA'S (WE HAVE TCASII) AND WAS SUBSEQUENTLY CLRED TO 6000 FT MOMENTS LATER. THE CTLR SAID I WAS IN A 'DANGEROUS POS' BEING 500 FT ABOVE MY ASSIGNED ALT. I REALIZE THE NATURE OF THE NEW YORK AIRSPACE AS IT IS VERY CONGESTED. I ALSO BELIEVE ANOTHER ACFT DEPARTING BEHIND ME HAD THE EXACT SAME PROB TRYING TO MAINTAIN 1500 FT. I WOULD HOPE DURING TIMES OF SEVERE WX THE DEPS AND ARRS OFF CLOSE ARPTS ARE GIVEN A WIDER MARGIN OF SEPARATION.