So in answer to an earlier question although Margaret Potts and William were not married until 1869 after his divorce from Sarah 7th Feb 1868, they were certainly involved together and had children including George Robson who named both William Weiland Robson and Margaret Potts as his parents on his marriage certificate in 1879.
Patrizia, it would have been most useful and time-saving to us if you had given this information at the outset.
Please can you say on which censuses you
have found George, and what is his age on each of them?
Have you tracked Margaret Potts' family to see if George is with any of them in 1861 or 1871?
There are a good many births of various George Robsons showing on freeBMD in County Durham - how many of these have you checked to see if they are 'your' George? ( we are, of course, making the assumption that he was born in County Durham which might not be the case).
I see that William and Margaret had two daughters living with them in 1871. Under what surnames were their births registered?