So, please don’t think I’m an idiot. Theoretically, if a pokemon was dual type for the same type would that make it 4 times weak but for times more powerful? So a Fire/Fire would be 4x weak against water and 4x as effective against grass… Right?

Um.  Do you mean, like, in terms of how the damage formula works?  Hang on; I’ll have a look… Go go gadget Bulbapedia…

“Type is the type effectiveness. This can be either 0, 0.25, 0.5, 1, 2, or 4 depending on the type of attack and the type of the defending Pokémon.”

Now, I don’t know whether the game has a lookup table for every possible value of that Type factor or just calculates it each time based on the type chart.  I suspect the latter, in which case if a Pokémon for some reason did have the same type twice, I suppose it would stack.

I can tell you that it would not get two doses of STAB.  The only possible values for that term are 1 and 1.5, so the bonus to Fire attacks would only apply once.

What… exactly would a Fire/Fire type… you know, be?  Something more fiery than a regular Fire-type?  That would be quite an achievement compared to the likes of Magmar, Entei, Reshiram, Volcarona, Heatran and Mega Charizard Y…