Sorry Jackie, I only have access to the 1881 Cencus, hopefully someone else can help out there.
I had a wee look through the British Vital Records CD's (much the same as the IGI) and found children born to:
John Allan and Agnes Aitken
John b. 01.05.1840, c. 02.08.1840
Agnes b. 12.08.1842, c. 22.08.1842
Bethea b. 03.08.1844, c. no date given
William b. 07.10.1846, c. no date given
Thomas b. 25.09.1848, c. no date given
Robert b. 08.04.1853, c. 08.05.1853
All born in Falkirk
Robert Stevenson and Helen Scrymegour Aitken
Helen Scrymegour Aitken b. 29.03.1850, c. no date given
William b. 30.03.1852, c. no date given
Henrietta b. 03.09.1853, c. no date given
All born Glasgow
I couldn't find anything for Thomas Hamilton Aitken or Margaret Douglas Aitken (Petrie).
Do you think there could have been a connection between Margaret's husband John Petrie Stevenson and Henrietta Petrie?
All William Aitkens born in Falkirk around the time 'your' William would have been born
William b. 01.04.1797, c 09.04.1797 to Robert Aitken and Elizabeth Hill
William b. 11.03.1801, c.22.03.1801 to Mark Aitken and Agnes Paterson - this couple had a stone in Falkirk Parish Churchyard
William b. 23.09.1801, c. 04.10.1801 to Adam Aitken and Catharine Gibson
(Falkirk Parish Churchyard was cleared and landscaped and there are no longer any stones)
Henrietta could have moved in with one of her children after William died so could be anywhere!
Anne