I haven't been able to find a Francis Holland baptised in Weymouth, but the following may be linked.
Francis' eldest daughter was called Eliza Rebecca Holland (she married in 1859). The Eliza was after her mother, but the Rebecca may have been after Francis' mother, making his parents John and Rebecca.
A John and Rebecca Holland are recorded as having several children in Wyke Regis, which is only a mile or so from Weymouth. John dies there in 1821 aged 68, and Rebecca in 1844 aged 76 (she is in the 1841 census with her son John).
The baptismal records have some of their children:
John (1799), William (1806) and Priscilla (1815). James, who dies in 1819 aged 11 may also be theirs, but there is clearly space for several more who have not been found. In 1815 John was described as a labourer rather than stonemason.
A Mary Holland marries Thomas Bussell in 1825 and Rebecca is mentioned in the banns (which fits as John has died by then) so she is another daughter; later censuses suggest she was born in about 1800. (Another Rebecca, bc1804, marries James Bussell in 1826 but there is no other evidence that she is connected).
Even if all of these are theirs (1799, c1800, 1804, 1806, 1808, 1815) there is still a gap around 1811 when Francis was born.
Nothing proved of course...
Richard