A corporate jet First Officer reported climbing through the 1500' restriction on the TEB RUUDY Two SID.

Narrative

Our flight was cleared from TEB to destination via the RUUDY Two RNAV departure. The Captain briefed the departure in these or similar words '...we'll cross WENTZ at fifteen hundred and then climb to two thousand...' as part of his takeoff briefing. I had no questions. After takeoff we were climbing via the departure SID and made our turn (260 degree heading) toward WENTZ intersection. We reached 1500' about two miles prior to WENTZ intersection; and continued climbing to approx 1700'; when New York Departure alerted us to our altitude deviation and re-cleared us to 2000'; rather than descend us back to 1500'. The altitude deviation was approx. 300' and 2 nm prior to WENTZ intersection. At no time was there any separation problem with other aircraft in our vicinity nor was there a TA or an RA; nor did I observe any targets on TCAS at 2000'. In fact; the Controller stated that traffic was held at 1500' on the RUUDY Two departure to avoid wake turbulence from heavy aircraft arriving at EWR; not to avoid conflicting traffic. Two ways to avoid this from happening again: 1) set 1500' in the altitude preselect; only setting 2000' passing WENTZ intersection; or 2) after takeoff; select RNAV mode and VNAV mode on the guidance panel; and set 2000' (or preferably 1500') in the altitude preselect.