Hmmmm...not sure if this will take a while for you, but you can go to Symbology -> Categories -> Unique Values, many fields.
That might help or at least get you started?
What about combining the two fields and then going unique values, one field?
Edit: then all the 1A and 2B and 3C, etc... values will be grouped?
Alright, I've got something going.
I've symbolized all of one category a certain color, and based on a different field had their size changed.
It's a mess right now, but hopefully it will help you out. Here goes:
In Symbology -> Multiple Attributes -> Quantity by category
Value Fields: choose whatever you want the color to change based on the field.
Symbol Size... choose the other field (for size).
Hit ok and see how it looks, then adjust accordingly.
Sorry I know it's not perfect, but I just learned it and figured I'd let you know haha.
Edit: I guess it's implied, but "Add All Values" then hit ok.