Is capillarity anti-gravity?

[ABC2019]

Yep ... there's more patience!

It is possible for the manipulation .... but I hadn't manipulated anything at all during the 1st experiment (object of the creation of this subject) ... my error was not to take photos at this time there (not thought ..)

a priori the reason why it seems impossible to me is the following: since the water rises in the wick, it is that at the interface between the pure liquid and the wick, the liquid prefers the wick and therefore rises.
For a drop of pure liquid to form and grow, the opposite is necessary: ​​that the liquid prefers the pure phase to the wick and descends into the drop. There is no reason why it should go up on one side and go down on the other.

In thermodynamics, this is called chemical potential: molecules move from a high chemical potential to a low chemical potential (just as bodies go from high potential energy to low potential energy, just like electric charges ( positive) range from a high electric potential to a low electric potential). This is not necessarily a "spatial" displacement, it is also the case when a chemical reaction occurs. The situation stabilizes when the potential is the same everywhere, and there is no more movement.

[Exnihiloest]

That's exactly it, ABC. The wikipedia article is clearly written:
"water adheres to the surfaces of the [capillary] tube to increase its contact surface with the glass and decrease its contact surface with air, then its molecules are attracted to the part of the surface of the tube immediately beyond, and by repeating this phenomenon the water thus rises along the tube".
When there is no longer any reason to continue because the water is at the end of the wick, the air all around no longer has any surface for a useful force on the water, and even that at the end of the wick force becomes opposite and greater than the force of gravity, water cannot even fall.

It reminds me of the tests of the "smot", a ramp with magnets which a ball goes up under the magnetic force or a track where it is accelerated, and of which the handymen hoped that at the end, it would be able to return to its point of departure, and so on.
It does not work of course any more, because it is the difference of potential magnetic energy between the departure of the track and the arrival which makes move the ball because of its magnetic potential more important to its starting position than the arrival. It is like hoping that a ball dropped from the top of an inclined plane and accelerating under gravity, will have enough energy at the bottom to go back up there. It would work in theory if there was no friction, but there is, and even if there was not the energy balance would be zero, we could not draw any energy from the system.
This is a general rule in the case of potentials: a difference in potential energy does not depend on the path followed. It only depends on the potential of departure and arrival. No cycle is therefore possible since then the starting and finishing points are identical.