Let $v$ be a weight on a domain $D$ in a metrizable locally convex space $E$ and $F$ be a complete locally convex space. Denote by $H_v(D,F)$ the weighted space of $F$-valued holomorphic functions on $D$ satisfying that $v.f$ is bounded, $A_v(D)$ subspace of $H_v(D,\mathbb{C})$ with the unit ball is compact for the open-compact topology. The aim of this paper is to study linearization theorems and approximation properties in several different topologies for weighted spaces $A_v(D,F)$ of functions $f\in H_v(D,F)$ such that $u\circ f\in A_v(D)$ for every continuous linear functional $u$ on $F$.