A bit more investigation into GW senior's whereabouts at the time of GWs birth is warranted
I thought so too but have my wicked suspicion he may have been up to no good (eating porridge) ?
or with another woman? 
I wish I knew! In 1871 he was in Great Driffield, East Yorkshire with his father & sister Jane, but by 1881 was living in Thornaby on the Durham/North Yorkshire border with sister Dinah and her illegitimate son, who had been born in Sledmere (Nr Driffield) in 1875.
His sister Jane married in the neighbouring town of Stockton in 1877 - just two weeks before GW Jnr's birth - and was living next door. I have her marriage cert but none of the Jackson's were witnesses.

The 1881 census states he was a widower but I haven't found any prior marriage, and when he married Margaret in 1882 he stated he was 35 and a bachelor.
Added: I have death certificate for what
may be GW's father, Robert, who died at 17 Thompson Street, Stockton in June 1873. The informant was George Jackson of the same address but it doesn't state any relationship so again, its somewhat inconclusive.