OK here goes,  I understand that center shot plays a very important role in tuning and a fat arrow such as a 2315 will aline different than a skinny arrow like a axis.  That being said how much difference will arrow diameter make in tuning?

I just don't get into the tech issues that much.  A fatter arrow will effect tuning but you just tune like any other arrow adjusting as needed.
I don't think you can put a formula on it or if it was possible I would not want to.
If you are looking to purchase arrows and need help deciding then posting the type bow and specs would get someone on here that knows the set up helping with choices.

If you're shooting a traditional style release (fingers) then arrow spine is even more important. If you swap to a skinnier arrow... read that as "much skinnier"... then you may have to build out your strike plate. Best bet is to do as Ron said... tune your arrow as needed... and your bow also.

If I shoot identically spined and weighted arrows, one a 23/64" wood and one a 9/32" carbon, the carbon will act weak due to it's reduced diameter (bow is tuned for 23/64").  I can't switch between the two without going lighter point weight on the carbon or building out the side plate as mentioned.  I think that is at least part of the reason that so many people shoot a stiff 75/95 carbon, the reduced diameter requires a stiffer spine than normal wooden arrows of standard 11/32 diameter.

Just my 2 cents based off of my experiments.