Do you have the deaths/burials of John and Anne?
The marriage at Cwm was in 1777, rather than 1778.
It says that John Roberts was of the parish of Dymeochion.
Which may be Tremeirchion?

Anne was of the parish (Cwm)
Both marked.
Marriage was by licence. Nothing so far to suggest that the bond/allegation are still around.
Baptisms at Cwm to John and Anne Roberts
John, 22 March 1778
Anne, 21 Aug 1779
Thomas, 12 Aug 1781
Peter, 3 Aug 1783
William, 2 Oct 1785
All bar Peter say that John was of (living at) Uwchglan
Did Anne junior die in 1781?
Speaking of Tremeirchion, there are a couple of John/Anne Roberts baptisms there later
Edward, 8 March 1791
Robert, 1 Sep 1793
No idea if they are connected, with Roberts being such a common name

John was a Labourer
Wife Anne was formerly Anne Bernard
Not a million miles away from Barnet perhaps (a musing, I'm being rather optimistic there!)
An Anne Bernard was bap 25 July 1756, at Caerwys, not far away (parents Thomas and Elizabeth)
EDIT Two more baptisms at Tremeirchion
Mary, 17 Jan 1796
Hugh, 5 May 1799