Whether you have traced back to Thomas and Ann (nee Ayles) Newman depends on how much proof you want. The censuses confirm that Robert (b Portland, rather than Weymouth - only the 1871 census says Weymouth) is the son of William Newman, master mariner, b c 1808.
The IGI only has submitted entries for an Edward Newman but the registers show a baptism in Jun 1806 for an Edward son of Thomas and Ann Newman. Is this your Edward? Probably, as there are no other baptisms, but I would want more proof: Newman is a common name.
There are some more entries that are worth following up:
Thomas Newman, buried 21 Jan 1848, Fortuneswell, Portland, age 82
Thomas Newman, bap Aug 1766, son of Edward and Sarah Newman (there is another baptism in 1764 with the same eparents suggesting that an elder son died, although there is no record of a burial).
Edward Newman buried 24 Jun 1792
None of these is definitely connected, but they are worth looking into.
Richard
PS A quick Google suggests that others are tracing this family.
