As Carrie notes, Stefan Bielinski of the New York State Museum discussed these names in a short essay "Veeder - Veder - Vedder". He said that all three of those spellings occurred in the Albany records as late as the 1790 census.
Bielinski said that over a period of 30 years he had "spoken with a number of people who claim to have their V's straight", but no one had "been able to divide all of them perfectly." He observed that the name Veeder was used in Albany city for "an essentially single but substantial household through time" (namely, the family of Simon J. Veeder, 1709-1786, his forebears and his descendants), while the names Veder and Vedder were found more in places surrounding Albany. In particular, he noted that the families "mostly known as Vedder appear to be descended from Harmen Albertse, whose large family spread out in the region especially in Schenectady," and included son Corset Vedder.
Other sources that have analyzed these New Netherland names farily extensively include Vader Genealogy (it seems that Vader is yet another spelling that evolved from these same roots) and Vedder in America, which is a subpart of the Dutch genealogy website Genealogieën van diverse families Vedder en Vedders.
I started this pursuit because I found that most of the children of the immigrant Simon Veeder had profiles with the LNAB of Vedder, which was troublesome to me because I had found these people's names in sources that consistently called them Veeder. It appears to me that this family was fairly consistent in using the name Veeder. However, daughters predominated among the chlidren of Simon's sons and paternal grandsons, so by the mid-1700s most of the living male-line descendants of Simon Veeder may have belonged to that one "substantial Albany household" that Bielinski describes. I propose that the LNABs of all of immigrant Simon's children should be changed to Veeder, and the name Veeder should be used in subsequent generations unless there is an indication that a particular person used a different spelling.
Similarly, the descendants of Harmen Vedder should be presumed to be Vedders unless there is good evidence to the contrary.