I don't have any further information about Rebeckah and her husband and child (or children).
"The Jaquith Family in America" does give information about her brothers Abraham and Jacob.Abraham apparently moved to Maine and may have operated a farm in Litchfield, Kennebec County, ME.He married 3 times and fathered 7 children.He is listed as having died in Mississippi, 26 Nov 1808.
Jacob seems to have lived and died in Fitchburg (d. 31 May 1847).He held a number of civic positions including hogreave, 1792; highway surveyor, 1810,1814, 1815, 1829; bondsman for the tax collector, 1814; field driver 1822; tithingman, 1831; and a deacon (Old Records of Fitchburg, 2:75; 5:3, 84, 87, 100, 220, 240, 339; 6:21).He married Ruth Putnam on 30 June 1791 - they had 6 children.
I have summarized both of these - not sure how much you are interested in the brothers.
The 1760s apparently saw migration to Vermont, since the Abenakis had been conquered and had moved to Quebec or had taken French names and were trying to maintain low profiles in Vermont.My branch of the Jaquith family moved to the Hartland-West Windsor area at that time.
After the Revolution, probably more people headed north to the "frontier".We have records of Jaquiths in Weston and Londonderry, VT and Jaqueths (still related) in Guilford, VT so they were an adventurous lot indeed.