The great majority of the inhabitants of Weener have been reformed (calvinistic), belonging to the Ev.-ref. church like in a number of towns in the western part of East Frisia (the part with strong connections with the Netherlands). A Lutheran church has only existed in Weener since the 1950s, the Catholic one since the 1840s.
The GEDBAS and Family Tree data says that the bride was born in Weener 1856. This might indicate that she was baptized in the reformed church of Weener. In this case (if you know that she was definetely baptized in a Lutheran church this would not be true of course) she should be in the Ortsfamilienbuch Weener (for ev.-ref. parish) and there is a good chance that the marriage is listed there as well.
Microfiches of the reformed parish registers (and all East Frisian Ortsfamilienbücher) can be checked at the Fachstelle für Familienkunde in the Landschaftsbibliothek Aurich. Unfortunately the Ev.-ref. church has not cooperated with Archion or any other online portal, so that most of the actual records are not accessable online.
From October 1874 on the civil marriage records would probably include even more and better data. It is possible that the GEDBAS/Family Free data is from the civil marriage record (and even possible that only the civil marriage happened in Weener). For Weener the Civil Register Records are at the State Archive in Aurich. Unfortunately they are as well (as far as I know) not accessable online.