  We prove an invariance principle for linearly edge reinforced random walks on
$\gamma$-stable critical Galton-Watson trees, where $\gamma \in (1,2]$ and
where the edge joining $x$ to its parent has rescaled initial weight $d(\rho,
x)^{\alpha}$ for some $\alpha \leq 1$. This corresponds to the recurrent regime
of initial weights. We then establish fine asymptotics for the limit process.
In the transient regime, we also give an upper bound on the random walk
displacement in the discrete setting, showing that the edge reinforced random
walk never has positive speed, even when the initial edge weights are strongly
biased away from the root.
