Hi Bill
First - apologies. 11pm at night and the old eyes don't do what they should (see the birthplace!!)
I've checked the 1851 and there is no George Hodgkinson with a birthplace of Burslem.
The 1861 has no George Hodgkinson but does have a George Hodgkins b 1848 Burslem - parents John & Harriet and siblings William, Thomas, Hannah & David
I've checked the image and it's definitely just Hodgkins
There are a few George Hodgkinson's but with different Staffs birthplaces - I've also checked Hodkinson and checked the Welsh 1851/61 as well just in case
A copy of his marriage cert will give his fathers name which will help to find him
These are the only 2 possible births on freebmd
Births Mar 1847 Hodgkinson George Leek 17 68
Births Sep 1847 Hodgkinson George Wolstanton &c 17 264