I have Tina Branford from the Dissidia line, and she came with these two black, solid circles that someone else described as being a little smaller than a soda bottle cap. Anyone know what these are for? They don't have any holes or joints and don't seem to attach in any way to the figure or the stand.

Those are included with some blind-box figures to make the box feel heavier, so that you can't compare and figure out what's inside just by "weighing" the boxes with your hands.  They have nothing to do with the figure itself - feel free to toss 'em.

That whole Dissidia series of figures is really great, too.  I just set mine up in my new apartment the other week.  Those, the Kingdom Hearts Formation Arts line, and the Final Fantasy Tactics set have been some of my favorites from the last decade.

oh lol i always thought those were for putting stands on if you had enough of them, if you wanted some kind of vertical staggered display.