  The weak splitting number $wsp(L)$ of a link $L$ is the minimal number of
crossing changes needed to turn $L$ into a split union of knots. We describe
conditions under which certain $\mathbb{R}$-valued link invariants give lower
bounds on $wsp(L)$. This result is used both to obtain new bounds on $wsp(L)$
in terms of the multivariable signature and to recover known lower bounds in
terms of the $\tau$ and $s$-invariants. We also establish new obstructions
using link Floer homology and apply all these methods to compute $wsp$ for all
but two of the $130$ prime links with $9$ or fewer crossings.
