Dear All,
A huge thanks for the various replies, and apologies for the belated response. I'll try to wrap everything up here.
Jane was born on 24 Jan 1846 and baptised on 20 Feb 1846, so more or less a month later, Some of her 'siblings' were baptised days after their birth, others were baptised three or four weeks afterwards. So I'm not seeing anything conclusive here. Also, the birth spacing of William and Amelia's children throws up no question marks around Jane's legitimacy.
Jane married Thomas Cope on 18 Feb 1871, and as AnthonyMMM indicates, the father of the bride is given as William Weatherby, so again no red flags.
I have, I believe, seen all of the available wills for the relevant Weatherby and Cope families, and likewise, I've found nothing yet to suggest that she was adopted. I haven't seen the Reverend Charles Stocker's will, but I'm reluctant to think he is involved in any way other than as a ward. Coincidentally, one of his daughter's eloped with one of Thomas Cope's brothers, and ended up in South Africa. It is said that the Reverend cut her off in his will, leaving her one guinea only. Perhaps rather fancifully I'm assuming his moral rectitude (including as a CoE rector) precludes him from being involved ...
DNA-wise, on Ancestry, if the Thru-Lines matches are to be believed, I would seem to be connected separately to both the Weatherby and the Caswell families at the level of the next generation back from Jane herself. Now, my understanding is that this might in theory be 'conclusive' proof, assuming that other people's trees in Ancestry are reliable (though this assumption is I guess not inconsequential)? Conversely, I haven't seen any DNA matches pointing to Revd Stocker.
And so, lastly then for now, thanks also for the pointers towards the records at Kew and the books by Susan Moore. I'll need some time to take a deeper dive with them.
richard