A couple of weeks ago, the Georgian Times published an article entitled "Demographic Information on the Abkhazian and South Ossetian Populations".
The data seems to be based on government (Tsarist Russian and the USSR) censuses so we can assume the figures are correct apart from the author's typos, (and possibly mine) and any errors and changes in the way the censuses were conducted and nationalities classified.
With those caveats, I have produced the following tables. The article was written in the old Soviet way, making lists of the figures so that no patterns are visible.
At first I could understand that Georgians were miffed when Abkhazia broke away as I had always thought that a lot of Georgians lived there. Then after reading a bit more and finding that Abkhazia had been an autonomous region of Georgia under the USSR, I could understand perhaps that they wanted to continue with some form of self-rule. Independence is catching, even if it isn't always economically viable. Look at the debates about whether Scotland could afford to be independent from England. The general feeling is that they missed the boat and should have declared independence when gas and oil were discovered in the North Sea. Now it is nearly all gone, they are a bit late, even though they can get lots of money from the EU.
Here is how Abkhazia developed as far as nationalities are concerned, according to this article (figures for the Abkhazian Autonomous Republic within Georgia):
No figures provided for Georgians to compare with that.
*calculated from the total minus the rest.
** total of the above, no total provided in the article.
Leaving aside the big differences in the two sets of figures for 1865 and 1866 and possible dispersal of Abkhazians in Turkey, the result seems pretty clear that most of the population of Abkhazia has been Georgian for a considerable time. Of course Abkhazians may have not bothered to classify themselves as such in the USSR, Georgian being good enough at the time.
But from those figures (admittedly produced by Georgians) it's pretty clear why Georgians lay claim to Abkhazia. Also it's clear why there were so many IDPs from Abkhazia, and why they were still not absorbed into Georgia proper, if the government didn't do much to help.
Now South Ossetia.
In 1989, South Ossetia, which only had the status of oblast' in Georgia, demanded unification with North Ossetia. In December 1990, the Georgian parliament declared South Ossetia no longer autonomous (sic), and began suppression of newspapers and bans on demonstrations. During the resulting fighting, according to the article more than 100,000 Ossetians fled from Georgia and South Ossetia to North Ossetia. The article says 10,268 of the South Ossetians now reside in Tbilisi. Which then raises the question of how many south Ossetians lived in Georgia and how many actually in South Ossetia during these years? And again, how many have reclassified themselves?
That leaves around 28,000 recently in South Ossetia who have either fled north or south again, or stayed in their villages. Claims of genocide have generally died down on both sides.
Of course nationality can be rather subjective question. In Istria, a peninsula containing Slovenes, Croats and Italians, people have responded to the nationality question in various ways over the decades. Many say they are Istrian first and anything else second. When fascist Italy took over Istria, it might have been politic to say Italian, and when the Yugoslav partisans came back, then Yugoslav was perhaps more useful. These days, when Croatia is not quite in the EU, European might be the best answer.