I've checked the 1881 census to try & locate William Henry but with no success (10 William Battys in Derbyshire alone).
The marriage certificate should give his age at the time of marriage & where he was living at the time. Let me have those and I'll try to narrow down the possibilities. There were only 6 Battys at Belper in 1881, including a William H, but he was only 11 months old. It could be that his father is a brother to your William but that's guesswork.
I doubt whether there is anything but a distant connection to my Battys in Killamarsh but if you can let me have the other information I'll check the census again.