The birth record at Jamestown identifies him as son of John & Mary Remington.
I am not positive that his marriage and data belongs to this Jonathan, but I am making an assumption, subject to further research. The will abstract is in the RI Genealogical Register, Vol. 7, No. 1. It identifies him as a mariner of Newport, and mentions his wife by name. No other family members are mentioned.
This must be correct because the Family Bible Record of Clemence (Remington) Cornell has this as his date of death. (Bible record courtesy of David Gips) However, her birth date for Jonathan is 10 Feb 1749, which differs from the town records.