Is adhesion responsible for the surface of the water in a graduated cylinder that is slightly curved at the sides?
It's more to do with surface tension......
Water molecules have a tendency to aggregate with one another (hydrogen bonding etc.). At interfaces this aggregation manifests as a "pull" from the interface to the bulk of the water, and this is why water forms spherical droplets.
At the water/glass interface other water molecules will try to associate with those at the interface. They do this as far as they are able to before gravity prevents further movement, thereby creating the curved meniscus.
So the biggest reason for the curvature is surface tension. Fill your cylinder with something like octane (which has a much lower surface tension) and you will not observe the same curve at the sides.