In cases like this, sometimes the only way is to look at both families, reconstruct them and assess every bit of evidence you can find.
Unfortunately there don't seem to be any wills that might help out.

William and Ann Orchard had the following children baptised in Whitchurch:
Elizabeth bp 26 Nov 1786
John bap 28 Oct 1788
Thomas bap 5 Jun 1791 (NB mother's name shown in transcript as Sarah but I think this might be a clerical error)
David bapt 8 Sept 1793 aged 3 mnths
Rebecca b 8 Nov bapt 15 Nov 1795
Mary b 7 Apr 1800 bp 11 Jun 1798
Charles b 15 May bp 8 Feb 1801
Ann b 26 Feb bp 27 Mar 1803
James b 26 Jun bap 20 Jul 1806
So if this is the James who married Letitia Golding, then he appears to have been the youngest child of William and Ann.
From a trawl of various record transcripts, I have come up with the following marriage:
William Orchard m Ann Head 31 May 1784 Whitchurch
There are the following burials recorded at Whitchurch:
William Orchard aged 60 30 Jul 1812
Ann Orchar(d) aged 76 24 Nov 1836
This is a possible for William's baptism at Whitchurch:
William 4 Apr 1762, son of David
Archer (no mother's name recorded)
Siblings:
Mariam 3 Jun 1764
David 10 May 1767
Thomas 5 Nov 1769
Mary 7 Feb 1773
There is a burial:
- wife of David Archer 8 Aug 1774 Whitchurch
I can't find a burial for David

?possible marriage:
David Orchard m Joanna Pearce 17 May 1759 at Burghclere
From HRO catalogue:
Settlement certificate stating that David Orchard and Johanna his wife are legally settled in Hannington, Hants, 4 Dec 1759
Moving forwards to see if any census helps, these are from 1851:
David Orchard b cir 1793, wife Sarah in Micheldever HO107/1673/12 p2, with family, recorded as a pauper
A James Archer recorded as deaf b Romsey aged 42 in Romsey extra 1851 HO107/1671/80 p 17 ag lab m Mary born in Tipperary Ireland, elder son Henry also born in Tipperary, daughters Jane & Emma b Romsey
William Archer b Chilworth, ag lab in Romsey extra in 1851 HO107/1671/116 p15 with wife Sarah & widowed mother Elizabeth aged 66 b Bentley. He appears to have been baptised 19 May 1805, son of James & Elizabeth Archer.
There seems to be much switching between Archer and Orchard - it was obviously subject a wide variety of pronunciation and accents.
Nell