I think the available evidence suggests Ellen is correct that the Jr. and Sr. are not based on parent/child relationships but simply used to distinguish two individuals with the same name. At the same time I think the evidence does suggest that Sarah did marry a cousin.
Allow me to start with 3 assumptions: 1) the sons in George's will are named in birth order; 2) the family followed typical naming conventions; and 3) given the predominant ethnic origin of the area, and the daughter named Hilletje, the family is of Dutch origin.
Using the assumptions above, George's father we would then expect to be named some form of Art. There is a 1769 will for an Aert Middagh of Rumbout precinct in Dutchess Co. (in Wills, Vol Aa, A, 1751-1796). In this will are named the beneficiaries Hester (wife), Hester LaRoy (grand daughter), Jacobus, Joris, and Geertie (children).
Let's note here that the normal anglicized version of Jacobus is James while Joris becomes George.
Let us skip ahead to Census 1790 where among the people enumerated at Fishkill, Dutchess, Co. we find: George Middaugh, Aart Middaugh Sr., Aart Middaugh Jr., Jacobus Middaugh Sr., and Jacobus Middaugh Jr.
The 1800 census of Fishkill contains James Middaugh, George Middaugh,, Aart G. Middaugh, Aart J. Middaugh, James G. Middaugh, and James J. Middaugh.
In Census 1810, under the surname spelling Meddough, we find Aurt G., Aurt J., James G., and James J. (and others)
While I can't say the exact birth order of boys and girls, and there is some guesswork that would need to be confirmed I would guess at a family tree that looks something like:
1. Aert Middagh (d. 1769) + Hester Unknown
1.1 Jacobus "James" (d. 1808 - see note 1) + Sarah unknown
1.1.1 Aart (aka: Aart St.; Aart J.)
1.1.2 Mindert
1.1.2 Jacobus "James" (aka: Jacobus Sr.; Jacobus J.; James Sr.; James J.) m. Sarah Middagh (see 1.2.5)
1.1.3 Hester m. John Tarpenning
1.1.4 Rebecca m. 1799, Baltus Carman
1.2 Joris "George" (d. 1800) + Elizabeth Peele (note 2)
1.2.1 Aart (aka: Aart Jr.; Aart G.)
1.2.2 Jacobus (aka: Jacobus Jr., James Jr., and James G.) m. Sarah Burhans
1.2.3 Paul (presumably the Paul Middaugh that died intestate in 1810 and possibly Husband of Catherine Masten)
1.2.4 Hilletje m. Peter Palen
1.2.5 Sarah m. Jacobus Middagh (see 1.1.2)
1.2.6 Hester
1.3 Geertie
1.4 Unknown daughter m. unknown LaRoy; died before 1769
1.4.1 Hester
note 1 - See Dutchess Co. Wills, Vol C-D, 1806-1815
note 2 - I have associated a 4 May 1755 christening for a Hester, daughter of Joris Middagh and Elizabeth Peele, birth given as 4 March, witnesses given as Aart Middagh and Hester LaMettere with this person. (ref: Poughkeepsie and The Flats, Book 39) - I would investigate further to see if the witness Hester is Aart's wife and George's mother.