Is there a reason this is so small?

A few lateral thoughts.
Given the texture issues (light, wobbly) that might make a larger diameter cake impossible, two other suggestions.
Make two 6 inch cakes to serve a larger group (either in two pans at the same time, or sequentially, removing one to a serving plate in the fridge while you make the second).
Make a German style cheesecake, which can sustain larger diameters and was reportedly the inspiration for Japanese cheesecake.
https://en.wikipedia.org/wiki/Japanese_cheesecake
https://www.allrecipes.com/recipe/87483/authentic-german-cheesecake/
https://food52.com/recipes/85308-kasekuchen-german-cheesecake-recipe

This is a hard one. I just took a look at this excellent, wonderfully helpful article by Alice Medrich (who thinks like an engineer, and who I've found consistently to be a reliable resource when trying to solve problems of this kind) https://food52.com/blog/13239-how-to-make-your-baking-recipe-fit-your-pan-size .

The area of a 6" pan is 29 square inches. If I were doubling this recipe, I'd use a 9" pan, whose volume is a little larger than 2 times the 6" pan. I'd be afraid that the 8" pan, with an area of 50 inches, would be too small. What makes this particularly tricky is the height of the cheesecake. As drbabs mentioned, this is a delicate cake - in large part due to the air that is beaten into the batter, and which serves to give the cake its lightness, or lift. Using a 9" pan probably won't give you quite the height as the single recipe in the 6" pan. I do think though that, given the structure of this case, going a little shorter will ultimately prove wiser than going higher. In any case, be sure to put a collar of parchment around your pan, if not using at least a 3" springform pan.

if you try it, please let us know how it turns out! ;o)

To go to an 8” pan, you’d have to double the ingredients. It’s such a delicate cake that I imagine the larger it is, the more risk there is for sinking or cracking. Certainly you’ll have to increase the cooking time. But I think it can be done. Good luck.