Regarding the information on the marriage certificate, 1895, -
"What are we looking for here, with Robert's information?"
Seeing that there is little information recorded by Elizabeth MACKAY about her origins might just be because.......... she knew very little.
Seeing that there is also little information recorded by Robert WALLER about his origins, when you know about his parents....place, date of birth etc. might be because.......
......the document that you have is a transcription of the civil registration, made from the original church record, and it was an incomplete transcription.
Elizabeth Marion MACKAY and Robert Alexander WALLER married at the Congregational Church at Marrickville, 1895, and this was recorded in the church marriage register.
The state needed a record of marriages, and the church marriage register would be sent to the BDM registration office in Sydney at the end of the year. A clerk would manually transcribe the church register to the civil register. Some of these transcriptions were incomplete ie the clerk cherry-picked what information to copy to the civil register and left out anything else because....... it was not important.
By the mid-1890s, and knowing that this incomplete transcription had been happening for about 20 years, the state registration office made effort to retrospectively add the missing information by again accessing the original church records, using volunteers to help.
This project was not completed.
Ordering a certificate from state records NSW for a marriage during ~ 1875-1895 will return you one of -
* a full transcription with all details.
* an incomplete transcription, which is what I suspect you have.
* an incomplete transcription, made complete with details added retrospectively, and notated to identify every amendment, date of amendment, and name of registrar ....giving authority to the amendments.
If you have an incomplete transcription, all is not lost. Knowing the name of the church, and Minister, and date, the researcher, that's you, locates the marriage register in a church archive, and you contact the church archive directly and request an image of the original.
Seeing how little information is also recorded about Robert Alexander WALLER is the clue to the possibility that I am suggesting, and so my interest in his details.
By way of example, and made with kindly intention, selective interest guided your response to my request for all the information on the marriage certificate. You are interested in Elizabeth, so gave only her details.
Thank you for including Robert's details, and it might offer possibilities for furthering your research.
There are contact details at this website that might be of use to you -
https://directory.archivists.org.au/index.php/uniting-church-in-australia-synod-of-new-south-wales-and-the-act-archives-office 