I'm not sure exactly what material weight you would need if using a tarp, but using premium quality 10oz vinyl baseball fields tarp (170 feet by 170 feet at a weight of 2300 lbs) as a basis for calculation, you would need more than 300 tons of tarp to cover the 175 acre reservoir, which you would have to ship to the site, deploy over the water, and anchor down somehow. The anchoring would have to handle all weather and wind conditions, and since its on water, you can't just put weights on top, so either you have to install posts throughout the reservoir to attach the tarps (not cheap), or you have to attach actual anchors to the tarps with depth ropes set correctly so as not to drag the tarps under. You could also tie the tarps together but that could also cause bigger problems if a big windstorm got a handle on it, like those videos of storms lifting and flipping the tarp at baseball stadiums during deployment.
Tarps lead to other problems too. Lets say you have to go out and make repairs on one of the posts or tarps in the middle of the reservoir; now you have to remove an entire series of tarps to get a boat to the needed area, and then redeploy those when you're done.
If someone happens to fall into the water, the tarp would pretty much be a deathtrap, just like when someone falls into a covered pool. If someone falls in with the balls, its no big deal.
The balls might cost slightly more than 175 acres of tarp in material costs, but cost of deployment and maintenance will be much lower. To deploy balls, all you really have to do is put them in, and they will spread out for you. To remove them, you just have a boat or equipment near that can scoop the balls up, or suck them out while putting the water back into the reservoir.