I finally got around to checking my census extractions and working Beckwith genealogy. I show Merwin T. BECKWITH as a possible son of Erastus Beckwith born c1800 CT, married 1st(?) 13 Jan 1823 Medina Co. OH to Elizabeth SPAFFORD (amazing how that name pops up in this family!), married 2nd Lucy W. FREEMAN 13 Sept 1838 Cuyahoga Co. OH. Location on census records and recurring names are my basis for saying possibly son of Erastus.
Erastus' line appears to be Thomas Jr-Thomas-Phillips-Jonah-Matthew-Matthew. If that is correct, it appears you are cousins to Merwin's descendants!
In "Beckwith Notes" v3 p49 Erastus and Elizabeth (Spafford) Beckwith are said to have had children: Merwin Phebe Electa Elizabeth Mary Frank
I show from census records (I have been unable to locate Merwin in the 1850 census!) Merwin's children to be: Franklin B.1848 OH Effie E.1858 OH Fremont E.Mar 1861 OH - although the cemetery records you post give died 1944 age 71, this means born 1873, but censuses clearly show 1861 birth year. Wallace1863 OH Gertrude E.1867 OH.
It would appear that Merwin and 1st wife may have had more children that just Merwin. Beckwith Notes lists several more girls.