Cook’s log states that he named Cape Weymouth and Weymouth Bay presumably after Viscount Weymouth but did not mention Portland Roads.
“On the Mainland within us was a pretty high promontory, which I called Cape Weymouth (Latitude 12 degrees 42 minutes South, Longitude 217 degrees 15 minutes); and on the North-West side of this Cape is a Bay, which I called Weymouth Bay.” (Cook’s Journal August 16th 1770)
Weymouth is next to Portland in England; Viscount Weymouth and Duchess of Portland were of the same family
The natural Portland anchorage is known as the Portland Roads.
Geoff Pope supplied a document from the British Hydrographic Department that states that the first mention of Portland Roads is in the sailing directions of Lieut Hemmings 1896 from Cape Weymouth to Torres Strait.
Cook named the Isle of Portland in NZ after the Isle of Portland in UK because it looked similar
The Duchess of Portland was a great collector of items that Joseph Banks collected on his journeys.