The tree also says John was born in Ashland, Wayne County, TN on 10 April 1818. ... If so, what Watson families were in Wayne Co. TN in 1810 and 1820?
But you have to work back one census at a time. Here is the 1840 census for the two Watsons in Gallitin County that show up in a search on familysearch. There is always the chance that there were others who were not indexed correctly.
Robert is probably in the western part of Gallitin County, the part that became Saline Co. I think Hugh is in the part that stayed as Gallitin Co.
1840 Census Saline Precinct, Gallatin County, Illinois
Robert Watson
2 males age under 5
2 males between 5 and 10
1 male between 15 and 20
1 male between 30 and 40
1 female under 5
1 female between 10 and 15
1 female between 20 and 30
see image 11 to id the location
https://www.familysearch.org/ark:/61903/1:1:XHB8-ZJC-------
1840 Census Bear Creek, Gallatin County, Illinois
Hugh Watson
1 male under 5
1 male between 10 and 15
1 male between 15 and 20
1 male between 40 and 50
1 male between 60 and 70
1 female under 5
2 females between 5 and 10
1 female between 10 and 15
2 females between 15 and 20
1 female between 30 and 40
1 female between 40 and 50
see image 7 to id the location
https://www.familysearch.org/ark:/61903/1:1:XHB8-ZTKThese men might or might not be brothers, with Hugh having his or his wife's parents in the home.
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Robert Watson shows up in Saline Precinct, Saline County in 1850, saying he was born in Tennessee:
1850 Saline Precinct, Saline County, Illinois
Robert Watson, 46, born in Tennessee
and family
https://www.familysearch.org/ark:/61903/1:1:M859-Q3LHe has a son John in the household. So if your John Curry Watson is a son of either of the two men, then he would be Hugh's son. But I'm not sure of that yet, and I haven't found Hugh yet in 1850, if he was still alive.