The initials identify the minister who officiated.
The first thing that struck me was how modern and consistent the handwriting looked, and how clean and spare each entry. And sure enough, the opening page for this book of NYC marriages has the note "copied from a volume labeled Record of Marriages ... copied by Sterling Potter 1902-3".
As the officient is a key piece of information in marriage records, and as only a few names would apply over a given time period, those names would be easy to record as initials or abbreviations, in a separate column, especially in a summary or index.
And on page 88 of 152 of the NY Marriages, Book 32 (at the start of the 1822 entries) is a key to some of those names. There may be additional key pages. There are number of pages for the 1830s where the officients' surnames are written in full or as abbreviations (not just 1 letter).
B. is Brownlee
D. is probably Dewitt, although Dougherty also appears in earlier entries
K. is probably Knox, although Kuyhers also appears in earlier entries
V. tbd [haven't found it written it full yet]