There is a mainly Sepharadic custom to do Birkat Kohanim under the Chuppah, but I can't seem to find a concrete source for it.
In Yalkut Yosef, Sova Semachot 8:5, Rav Yitzchak Yosef merely addresses why it's not an issue to say Birkat Kohanim outside of Chazarat HaShatz or orally, in general. He does not actually give a source for the Minhag, though. Nissuin Kehilchetam (12:67 footnote) points out that it's a strange Minhag that caused some strife between Rabbanim in America sixty years ago. Specifically, Rav Altusky was very upset at a number of Gedolei Yisrael whom he saw do it, and Rav Shlomo Zalman Katz responded, as printed in HaPardes, vol. 28, Simanim 20 and 32. The Nissuin Kehilchetam also cites a Khina veKhisda vol. 1 page 138 amud 4, but it doesn't seem to be relevant (it's about Shehasimcha bimono). I've included parts of the findings below, but it's not at all satisfying.
(Edit: It seems that at a wedding, the custom is for Kohanim specifically to be called up to bless the couple, not Yisraelim.)
Could someone point me towards a source?
Yalkut Yosef, Sova Semachot vol. 1, 8:5
ה. מה שיש נוהגים לברך את החתן והכלה תחת החופה, בפסוקים יברכך ה' וישמרך וגו', אין בזה שום חשש איסור של אמירת פסוקי הכהנים על ידי ישראל. וגם אין לחוש בזה משום מה שאמרו דברים שבכתב אי אתה רשאי לאומרם בעל פה.ה)
[Insert long footnote]
First page of Rav Altusky's article, HaPardes vol. 28 Siman 20
Rav Shlomo Zalman Katz's response, ibid Siman 32
