Bar stools are light one at a time but a full set adds up fast, and stacking them carelessly is what actually causes the damage, not the carrying. A few minutes of padding between each stool saves the finish.
Pro tip: Number each stool with a small painter's tape tag if they are part of a matched set with slightly different wear, so they end up back at the same spots.
Watch out: Do not stack more stools than the bungee cords can hold snug; a loose stack shifts in transit and can scratch every stool in it.