Depends on ammunition/sling type for me.
Lighter/thinner slings are more efficient as less air resistance and less mass to rotate. However, when using heavy stones the relative weight of the sling is less compared to payload, and you will typically be swinging at lower speeds anyway so those disadvantages are less significant. Thinness also tends to cost in ease and speed of use, for example very thin slings will tangle a lot and generally be a pain. On the other end of the spectrum thicker braided slings pretty much spring into aligned state. Paracord is a good middle ground which doesn't tend to tangle and is still pretty efficient.
I've also found that heavier/thicker slings are more stable- i.e. the pouch cannot roll on it's axis and dump bigger stones (with higher centre of mass) out of the side- this is something that can be difficult to achieve with leather/paracord to 100% reliability, and typically you trade off with length of pouch and ease of release.
Durability is also a thing, though mostly for natural slings. I wouldn't trust a natural fibre sling below a certain thickness, even sisal has it's limits. So if you like natural slings you can't go too thin.
IMO heavier slings should always be tapered to give a much lighter/cleaner release. Non-tapered heavy slings are uncomfortable to use. Also who doesn't love the whipcrack