In D'varim 22, the pasuk commanding placement of tzitziyos on 4-cornered garments immediately precedes the pasuk describing/commanding getting married. The juxtaposition gave rise to the minhag of simultanaizing these two acts.
(Extracting instructive meaning from the juxtaposition of two verses is universally acceptable as a method of interpretation only in D'varim. The example used by the g'mara to prove this includes one of the aforementioned p'sukim.)
Extensive justification for this practice appears in this Satmar publication: פרי תמרים