  According to Kat\vetov (1988), for every infinite cardinal $\mathfrak m$
satisfying ${\mathfrak m}^{\mathfrak n}\leq {\mathfrak m}$ for all ${\mathfrak
n}<{\mathfrak m}$, there exists a unique $\mathfrak m$-homogeneous universal
metric space $\Ur_{\mathfrak m}$ of weight $\mathfrak m$. This object
generalizes the classical Urysohn universal metric space $\Ur =
\Ur_{\aleph_0}$. We show that for $\mathfrak m$ uncountable, the isometry group
$\Iso(\Urm)$ with the topology of simple convergence is not a universal group
of weight $\mathfrak m$: for instance, it does not contain $\Iso(\Ur)$ as a
topological subgroup. More generally, every topological subgroup of
$\Iso(\Urm)$ having density $<{\mathfrak m}$ and possessing the bounded orbit
property $(OB)$ is functionally balanced: right uniformly continuous bounded
functions are left uniformly continuous. This stands in sharp contrast with
Uspenskij's 1990 result about the group $\Iso(\Ur)$ being a universal Polish
group.
