Good evening

I am trying to find get further on the tree of an Edward Browne. I have his gravestone inscription, where he died in 1869 aged 70. I have a marriage date of 1835 (but no physical record) to a Mary Eliza Gillman, and a record listing for wills for both of them. I have managed to go back with Mary Eliza, as she appears to be peerage. But Edward Browne seems to come out of nowhere!
I can't pin down where they actually got married. Her father had an address in Dublin, Bellevue House, Booterstown; and it appears this house may have been left to Mary Eliza, as Edward Browne is listed with this address also.
Some time between 1855 and 1860, Edward Browne purchased a property in Rosleague, Co. Galway. He had a son, Gillman, who was born around 1836, but I can't find a birth record for him, to pin down where he was born. Gillman was listed on his grave as the eldest son, so I assume they had other children too, but, can't find them either!
Edward and his son Gillman were Justices of the Peace for Galway, and there are plenty of mentions in old newspapers.
Despite this, I seem to be going round and round in circles, trying to get that one step further back.
Any advice?
Thanks in advance.