Spinning or not, extra weight can only make any difference during acceleration. If you maintain a constant speed, no amount of weight will make any difference.

It matters a lot how good the wheels are too. My bike came with 36 spoke wheels and the rear was popping a spoke about once every week or two when new. I rebuilt with the same hub but with better spokes and a good rim, and it never even went out of true again, over the course of 4 years and about 15,000 miles (eventually the axle broke).

All of my spoke breaks were at the elbow, so I suspect the spokes were under-tensioned at the factory. Also the rim was crap, a single-walled very thin job. I replaced it with a Mavic MA-3. When I rebuilt the front for discs, I used an Alex Adventurer. When I built a new wheel on the back due to the axle breaking, I used a Salsa Delgado Cross rim. These have all been very durable.