Did any of your Williamses emigrate?
Not to my knowledge, although I don't know a lot about them.
My great grandmother Gwen was widow of Hugh Williams(1856), whose family farmed at Pen Rhiw, Dolwyddelan. ( I already have a Rootschatter connection for this family).
Gwen had 2 sons, Robert (1880) and Griffith (1886), living with her in Pentre Bont in 1891. Robert was a quarryman by 1901, still living with her and second husband in Blaenau Ffestiniog, whilst Griffith was a farm worker at Hafod Gwennlian, nr Roman Bridge. I believe Griffith went on to have a daughter Gwen but that's all I know. They would be my grandfather's half-brothers.
Bronwen