Eliza Ward - is this the answer? (General)
Yes, maybe he was her father and the vicar insisted father not put on baptism as she was born out of wedlock.
I have someone in my tree who was born illegitimately, baptised 6 weeks after birth and on the same day his mother married, so I am sure who she married was the dad. Photos show the resemblance anyway. :)
Simone xx