Hello and a warm welcome from me too

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Re: the marriage record....
The word would not be "elder" son/daughter. Majeur/majeure means that the groom/bride were of the age of majority, which I believe in those days would have been 21 years. William and Mary Bayliss were both deceased. Anne and Ellen declared that they were unable to write their names in the record.
Do you have the family in any census? These records (depending on the year) usually give place of birth for the citizens and/or their parents.
Do you have death dates for Thomas and Anne?
I am assuming from your earlier post that you have all info going forward from the marriage to the present and are trying to trace backwards from this point?
PB