Well, sorry to say it but you are completely wrong. Two things to consider, a 115-grain projectile will use more powder to achieve the velocity needed to produce similar results to a 147-grain projectile. Increased powder charge combined with increased velocity produces more recoil. I will spare everyone a long math example.
But if you want to verify, just calculate recoil energy (google for assistance). As an example: on my Tanfoglio Stock 2, the 147-grain projectile will generate 2.88 ft.lbf of recoil energy, while 115 grain projectile out of the same gun generates 3.21 ft.lbf.