That a superfluid rises in a tube doesn't mean that it doesn't have any weight; it means that there's another force present, that acts in the opposite direction and more than compensates the superfluid's weight. Cf. here: Article The onset of superfluidity in capillary flow of liquid helium 4

The superfluid-atoms have a weight (otherwise we must reconsider the General Relativity). The climbing is a consequence from the atom-atom-coupling; the atoms form a chain coupled by very weak (but non-zero) van der Waals forces, so lower atoms can pull the upper ones over a wall (of course, it works in the gravitation only). The atom chain doesn’t break because the motion of every atom is frictionless.

Dear Professor Dolgopolov,

Thank you for your very interesting answer.

Your conception reminded me of that of Einstein's in connexion with how he understood a supercurrent :

"One of the earliest was Einstein (2), who in 1922, envisioned a chain of molecules, each passing an electron from left to right along the chain: “ It seems unavoidable that superconducting currents are carried by closed chains of molecules (conduction chains) whose electrons endure ongoing cyclic exchanges”.

Extracted from :

http://dx.doi.org/10.13140/RG.2.2.17687.60326

However, my conception is non-particulate, and so these considerations do not necessarily apply, viz :

"Moreover, in what follows, we want the reader to perceive of a ‘ telegraphing of amplitudes,’ rather than the ‘flow’ of physical matter."

Stam Nicolis

Dear Professor Nicolis,

Thank you for your interesting post, and link.

"another force present, that acts in the opposite direction"

But I would contend : how can a force act upon something that -by definition- cannot be acted upon by a force?

The superfluid flow, like a supercurrent flow can flow forever-- presumably, because no force can act to retard it-- it is -absolutely- resistance-less

Unless, you are saying it can be acted upon by a force? ie. it can be retarded, and is not -absolutely- resistance-less?