Stalin knew perfectly well that Georgia was a tiny part of the Soviet Union and that you couldn't run the Soviet Union with Gerogians alone. According to Khrushchev, Stalin said toward the end of his life: "Who will we appoint chairman of the Council of Ministers after me? Beria? No, he is not Russian, but Georgian. Khrushchev? No, he is a worker, we need someone more educated. Malenkov? No, he can only follow someone else's lead. Kaganovich? No, he won't do, for he is not Russian but a Jew. Molotov? No, he has already aged, he won't cope. Voroshilov? No, he is really not up to it. Saburov? Pervukhin? These people are only fit for secondary roles. There is only one person left and that is Bulganin."
https://books.google.com/books?id=p2AdDAAAQBAJ&pg=PA44
The reference to Beria being unacceptable because he was Georgian rather than Russian may seem strange from Stalin but it refleccted his awareness that after him it would be almost unthinkable (absent an outright coup by Beria) for *another* Georgian to be top man in the USSR. It would give Georgia a vastly disproportionate role.
Moreover, although he was fond of Georgian songs like "Suliko" and of classic Georgian literature like Rustaveli's *The Knight in the Panther's Skin*
https://en.wikipedia.org/wiki/The_Knight_in_the_Panther's_Skin and although he always spoke Russian with a Georgian accent, it is a mistake to see Stalin as *politically* partial to Georgians. In criticizing the anti-centralist tendencies of some Georgian Communists in the 1920's he referred to Georgia rather condescendingly: "I have a notion that certain comrades who are working in a certain piece of Soviet territory called Georgia are not all there in their upper storeys..."
https://www.marxists.org/reference/archive/stalin/works/1923/04/17.htm After World War II, "one day Stalin suddenly asked Beria why all his generals and security staff seemed to be Georgians. Beria answered that they were devoted and loyal. Stalin said angrily that not only Georgians but also Russians could be loyal..."
https://books.google.com/books?id=rSgfbK0hi2UC&pg=PA257
And Stalin's paranoia (if it can be so characterized) would hardly leave him less suspicious of his fellow Georgians than of other nationalities. This is a man who after all had purged Georgia's leadership as much as that of any of the Soviet republics, who had virtually forced Ordzhonikidze to commit suicide, and who very likely was going to purge Beria, too--in Stalin's last months, the security organs were accused of "insufficent vigilance" against the "doctor-plotters"--and under Stalin being accused of "insufficient vigilance" was often a prelude to being accused of actual complicity.