Back then there was a much better resource than the federal decenniel census (as many of them were rudimentary and only told the number of household members for purposes of determining congressional representation). Each state was allowed to do its own census in a year not ending in zero. New York opted to do them in years ending in "5" from 1825-75 (good timing for you). Here's a list of the counties available on microfilm through the LDS in a given year: http://www.nysl.nysed.gov/genealogy/nyscens.htmhttp://www.nysl.nysed.gov/genealogy/nyscens.htm
P.S. When you're searching for the name Tessier, realize that many F/C's pronounced it Tacy or Tacia. There are many attrocious versions of the name in both federal and state censuses because the census takers often did not have any background in the French language...so they just wrote down whatever they heard.