This is terribly confusing - who invented this labelling system? I always tell people two things to remember how sizing works. The older I get, the thinner I get. If you knew me, you know this isn't true, but why get in the way of a good mind trigger. It should remind you that the higher the number the smaller the bead or wire. So a size 13 seed bead is way smaller than a size 6. As another example, 24 gage wire is way smaller or thinner than 16 gage wire. Of course, this is really just for seed beads and Delica beads - most other beads (gemstones, glass) are labelled by true measurements, such as 3mm diameters, etc.
As for thread sizing, I actually think of these the same as bra sizes. A is the smallest, B the next smallest, then D, then F. Of course, then someone decided A wasn't thin enough, and created O and OO. I think of the OO as a pair of glasses, as in - I can't see this! That is how I remember that OO is the very smallest, O the next, and then A, and so on. It is a ridiculous system and now I am going to spend way too much time on Wikipedia to figure out how it evolved. This of course, doesn't apply to bead wire (which is marked as Fine, Medium, etc.) or silk on a needle, which actually uses the opposite system with the higher number being the thickest. Really.