  Two-dimensional systems have strengthened their position as one of the key
materials for novel applications. Very recently, boron joined the distinguished
group of elements that are confirmed to possess 2D allotropes, named
borophenes. In this work, we explore the stability and hardness of the highest
boride of tungsten, which is regarded as built of borophenes separated by metal
atoms. We show that WB$_{3+x}$ has Vickers hardnesses approaching 40 GPa only
for small values of $x$. The insertion of extra boron atoms is, in general,
detrimental for WB$_{3}$ in terms of hardness since leads to the formation of
quasi-planar boron sheets that are less tightly connected with the adjacent W
layers. Very high concentrations of boron ($x \approx 1$), give rise to a soft
(Vickers hardness of about 8 GPa) and unstable $hP$20-WB$_{4}$ structure that
can be considered as built of quasi-planar boron $\alpha$-sheets separated by
graphitic W layers. On the other hand, we show that the formation of tungsten
vacancies brings on structures, e.g. W$_{0.75}$B$_{3+x}$, with Vickers
hardnesses that are less sensitive to variations in the boron content and are
close in value to the experimentally reported load-independent values above 20
GPa.
