Thanks Gortinanima!
I like to check here before running off and doing a lot of research as someone might have already done so. No need to plough someone else's field so to speak. I got little feed back to I assume not much has been done on this family.
Your baptism entries points to something I found in the Registry of Deeds records which suggest Katherine was a second wife. A memorial dated 14 September 1739 records a lease of 3 lives of which one was Henry Makiliwaine, 7th son of Andrew Makiliwaine of Londonderry, barrack master [Ireland. Registry of Deeds. Vol. 100, p. 469, no. 71273]. If the same person, then he had 4 sons by a previous wife.
Andrew seems to have married a 3rd time. This time to Lucy Noble of Derrygree, County Fermanagh. His marriage articles with her are recorded 27 September 1746 and in it her refers to a Lease granted to him of a tenement on Bishop's Street where he lives which was for his life and the lives of his sons John and Henry [Ireland. Registry of Deeds. Vol. 123, p. 489, no. 84619].
McIlwaine/McElwain/etc. does not seem to be common about Londonderry. Were there other baptisms in St. Columb's records? This is something I do not have access to.
My interest in the McIlwaines is because there is a 1734 marriage licence bond made for the marriage of John Kinkead and Elizabeth McIlwaine [Index to Raphoe Marriage Licence Bonds, 1710-1755 and 1817-1830. Transcribed by Rosemary ffolliott. Dublin: The Irish Ancestor, 1969. Published as a free supplement to The Irish Ancestor. 8].
Andrew's 1746 marriage to Lucy Noble is interesting, because in 1732 there was a John Kinkead of Aghansillagh, Drumachose Parish married to a Jane Noble who I can find no further trace of. Perhaps he is the same person as the John Kinkead who married Elizabeth McIlwaine in 1734.
Regardless, I sure appreciate any information that helps sort out the McIlwaines about Londonderry City in the early 1700s. I can and will continue to search the Registry of Deeds and Derry Corporation records. Outside of that, tidbits are appreciated!