I am trying to bare shaft tune my new bow. I think that the arrow is showing slightly stiff. If I ad fletching is this going to weaken the spine enough for me to notice? Also will adjusting the brace height affect how the arrow shows week or stiff?

Adding fletching will make it show stiffer. Increasing the brace height may also make it show slightly stiffer. Brace height does the opposite of what it seems like it ought to.  If you want to weaken the effective spine of the arrow add weight up front, or lenthen the arrow.

I thought adding weight to the back would make it weaker

Nope, weight on the back stiffens effective arrow spine. Slightly weak, add fletches, maybe a wrap as well. Or a little more up front. Or don't cut them so short, or, or, or, lots of options. Have fun and stick with it.

http://www.acsbows.com/sitebuildercontent/sitebuilderfiles/tuninglongbowsandrecurves.pdf