There are two possible marriages for William Barber to a Henrietta around that time.
23 Sep 1816 at Racton (near Chichester) to Henrietta Eagle witnesses Jn PESKETT Eliz BASSETT
and
28 May 1817 at St Pancras, Chichester to Henrietta Deacon
It won't be easy to tell which is the right one and neither are very near to Falmer.
William is shown as a labourer on John's baptism at Falmer on 17 Aug 1817 and the date of John's birth is given as 9th August.
Do you know if your John had siblings?
There is another baptism at Walberton. Again, nearer to Chichester.
Entry from Walberton St Mary 1813 - 1901
First names Henry Barber
Sex s Baptism 08-Feb 1824
Father William Barber Occupation Razor Grinder
Mother Henrietta Barber
This latter couple also had Richard. Baptised West Tarring in 1819. William was a cutler then so same line of work and Elizabeth in 1821 at Birdham. He was a razor grinder then.