Here is a Nietzschean perspective, from Heidegger, Off the Beaten Track (pages 170-171 & 184)
The essence of value is based on its being a viewpoint. Value means
that which one has in mind [ins Auge gefasst]. Value is the point of
sight for a seeing that has its eye on something, or, as we say, that
counts on [auf etwas rechnet] something and thereby has to deal with
[mit anderem rechnen] something else. ...
In characterizing value as a viewpoint, the one essential thing for
Nietzsche’s concept of value follows: as a viewpoint, value is always
posited by a seeing and for a seeing. ...
Value is value provided it is valid. It is valid provided it is
posited as what matters. ... All beings are representing beings to
the extent that nisus is part of the being of beings: nisus, the urge
to make an appearance, the urge that enjoins a thing to arise
[Aufkommen] (appear) and so determines its occurrence [Vorkommen],
The nisus-like essence of all beings takes and posits for itself in
this way a point of sight. The point of sight provides the perspective
which it is essential to follow. The point of sight is value.
On 'moral or axiological claims' such as justice:
Nietzsche does not at all understand morality as something determined
in the first place within the ethical and juridical realms. Rather, he
thinks morality on the basis of the being of beings in their entirety,
i.e., on the basis of the will to power. What is just [das Gerechte]
is in accordance with what is right [dem Rechten]. However, what
is right is determined on the basis of that which is in being as a
being. That is why Nietzsche says (Werke, vol. XIII, "Nachgelassene
Werke," §462, from 1883): "Right = the will to make a momentary
power relation obtain eternally. To be satisfied with that power
relation is the pre-condition. Everything venerable is called in to
let what is right appear to be eternal."
So the axiological claims are made from what the observer feels strongly about; being certain of certain values, and staking a claim on them.
Last word from Buddha:
That brahmana who does not grasp at a view, with what could he be identified in the world?