It certainly appears to have gotten a quadruple rating as you note. The distance appears as though it should be just under 150 miles, which agrees with 12 1/2 cents for a single rate.
From the 1825 Postal Laws & Regulations (PL&R):
and for every packet composed of four or more pieces of paper, or one or more other articles, and weighing one ounce avoirdupois, quadruple those rates
If you just have 1 sheet and its well under one ounce, then I would suggest that maybe at the time of mailing there were other "articles" attached, so to speak, getting it up to one ounce.
Does the content of the letter imply other materials being sent / included?
edit: Also, what is the dateline on the letter? Did it originate in Syracuse, or somewhere else? Steam and way letters are usually rated for distance from the point of origin.