Yes and no. Since heavier gloves are *ahem* heavier, the effort of keeping your gloves up and punching repeatedly will wear your arms and shoulders out faster than lighter gloves. This may hurt more during training, but it will make competition gloves feel lighter and faster in the ring.
If you aren’t planning on competing, heavier gloves are still a good idea. The added padding makes heavier gloves more effective at keeping your hands safe and comfortable during training sessions.
To sum up: they add pain from arm fatigue, but the less the odds of injury fatigue, so the benefits far outweigh the costs.