Suther, read up about sighting in revolvers. Bullet weight does matter as it controls the amount of time the bullet is in the bore and at what point it leaves the muzzle during the rise from the recoil. A .357Mag revolver loaded with a mix of .38Spl and .357Mag even with the same bullet will print the Magnum rounds on target in a group that is lower than the slower .38Spl rounds despite reaching the target sooner due to the higher muzzle speed. This occurs because the Magnums leave earlier.
It's very noticeable as well. At around 15 yards the difference is about 2 to 2.5 inches.
The same thing occurs in semi autos as well. But not to the same extent because the slide and barrel start moving back in a straight line first. And by the time the recoil is felt to a significant degree in the lower frame through the recoil spring the the bullet is long gone. But there's still a small amount that shows up. If you get your 9mm sometime soon and shoot some 115gn, 124 and some 147gn ammo you'll find that the faster 115's tend to print a group that centers about 1 to 1.5 inches lower than the 147's at around 15 to 20 yards.
I know from your other posts that you're used to shooting rifles. And rifles, thanks to the much higher weight, longer mass moment arm lengths and better support, do not suffer from recoil related bullet rise issues. But handguns are a different zebra.