I don't know if you have had any answers to your query. There are Fleming's in Arkona Cemetery, but they don't seem to match what you are asking for. There are no Southworth's listed at all. Here is what I did find.
John Fleming died June 17, 1861 age 71 yrs. & 10 mths
Mary J. fleming (illegible)
Eliza Ann, daughter of Wiliam & Mary Jane Fleming died May 11, 1859, age 3 yrs. & 2 mths.
Lot 6----William Fleming (lot owner)
I did find the Wight's. It looks like Albert G. was married twice.
1 Alla Theo White, wife of Albert G. Wight 1868--1930
2 Rachel M Wight, 1876--1877
Frederick Wight, 1878--1878
3 William Wight, 1841--1924
4 Sarah A. Rumford, wife of William Wight, 1848--1936
Lot 5 - Peter W. Wight (lot owner)
I would say the two young children were buried in the same plot.
1 Floyd L. O. Wight, husband of Minnie Fuller, Mar, 1901 -- Aug. 1969
2 Albert G. Wight, husband of Mary C. Dow Sept. 1870 -- Jan. 1965
3 Mary C. Dow, wife of Albert G. Wight Nov. 1872 -- Apr. 1958
Lot 5E -- Floyd Wight (lot owner)
In spite of the lot numbers, I don't think these plots are side by side.
Lot 5 -- Peter W. Wight is in Map II Range 3 & 4
Lot 5E -- Floyd Wight is in Map IV Range 2
I hope this is some help to you.
Jim & Elaine Ward
54 Albert St.
P. O. Box 1262