It took me some time to convince myself that answer (B) is correct. Here is my reasoning:
It is not enough to say "the liquid would spill out of the top if the top wasn't there" - because the middle of the liquid is lower, and you can't decide just from that piece of information whether those two effects balance out, or whether one is bigger than the other.
In the steady state scenario, viscous forces in the liquid have eliminated velocity gradients in the liquid until the velocity of the liquid is strictly proportional to the distance to the center of rotation. Once that happens, the liquid that's not on the axis is experiencing an acceleration - which means that there must be a force on the liquid, and which means there must be a differential pressure across the liquid in the radial direction, and the differential pressure scales with $r$ - the distance to the axis.
Now if we had a cylinder that was a little bit taller than the liquid level, this pressure differential would result in a slope on the surface of the liquid that is a function of $r$ - specifically, the slope would be proportional to $r$ so the surface takes on the shape of a parabola (ignoring surface tension effects). See https://physics.stackexchange.com/a/88344/26969 for a derivation, or http://www.mne.psu.edu/cimbala/Learning/Fluid/Rigid_body/rigid_body.htm for a more complete analysis including pictures.
Here comes the "bit of insight" that I needed:
Imagine you start with the open container. When it is rotating, the surface will be curved but the only force on the bottom of the container is the force of gravity pushing down on the liquid - in other words the total force on the bottom is equal to the weight of the liquid.
Now we start moving the lid down. When we first touch the water, we start to experience a force - we have to push down against the pressure of the water in order to push down the lid. As we push, the water is pushed inwards. Now in pushing on the lid, we are applying an additional external force on the liquid in the vessel - and so there must be an additional upward force by the bottom of the vessel on the liquid to keep things in equilibrium.
This diagram tries to explain it - the numbers are fictitious: