Barrel droop is caused by improper machining of something in the breach area, it is not a function of barrel weight. If the barrel is heavy enough that it causes droop, that means that it is actually starting to "cock" the gun on its own... in which case you've got a severely weak barrel lock-up!
Longer barrels do impact accuracy, although I suspect it has more to do with the sight radius than anything else, at least whey you're only talking a couple of inches on the length of a rifle barrel.
As the distance between the sights gets shorter, a slight mistake in aligning the front and rear sights translates into a greater aiming error... basic trig, ya know. That's one of thechallenges of pistol shooting.