Hello Och Aye,
Welcome to the site. Unable to help you on the birth of Archibald side. Had a look and could see nothing.
However, in case you didn't have them, on
www.scotlandspeople.gov.uk at the bottom left of the page under the wills etc. there is a will and an inventory for 'your' Ann. Cost £5.00 each to view and download - via 'cart' system. (I did a search for Heughs from 1840 to 1901).
The doc at the bottom will be 'your ' Archibald. I see that in the 1841 census he's a shoemaker. Also £5.00 to download. Good luck. Regards, Steve

HEUGH ANN 07/06/1900 OR RUSSELL, GROCER, &C., DUNBAR, D. 12/12/1899 AT DUNBAR, TESTATE INVENTORY ONLY HADDINGTON SHERIFF COURT SC40/40/32
HEUGH ANN 07/06/1900 OR RUSSELL, GROCER, &C., DUNBAR, D. 12/12/1899 AT DUNBAR, TESTATE WILL HADDINGTON SHERIFF COURT WILLS (FROM 1898) SC40/43/2
HEUGH ARCHIBALD 05/11/1862 BOOT AND SHOEMAKER IN DUNBAR HADDINGTON SHERIFF COURT SC40/40/14