Again, working off questionable transcriptions, I think this is the family, without John in 1861:
William Hay 43 cotton weaver b. Carluke
Caster Hay 34 b. Lanark
Robert Hay 14 cotton weaver b. Carluke
Alexander Hay 9 b. Carluke
William Hay 6 b. Carluke
Catherine Hay 2 b. Lanark
Address: North Vennal, Lanark
Closest I can get so far for John in 1861 at the moment:
John Hay 15, boy on farm, b. Lanark working at the farmer Stark's household in Over Williamston, Midcalder, Midlothian.
There are a few other possibilities perhaps also under Cunningham.
At this time, remember that names were always very fluid (not just in terms of spellings but also how people changed surnames around) so it wouldn't surprise me to find John under Cunningham or Hay for example. If we have the right entry, his mother Esther's new husband (if she was actually married to Robert Cunningham before) would have been around from when John was very little.
Who were the witnesses to John's marriage from his cert.?
Monica