Also have this problem; I just trim the arm hair with a #1 blade on a trimmer.... leaving really short hair. Do not, I reapeat... DO NOT shave completely, you will &@#%ing regret it. Also, very important, wear undershirts. Not wife beaters, but actual t-shirts under your shirt that cover your pits. It will absorb all the sweat and not show through as much. I stopped doing deodorant with Anti-persperant, because It would work for a couple of hours, and then it would be like the hoover damn broke.... Then there would be a constant stream of sweat running down my sides I crap you not.
BTW, I'm not fat.