  In this paper we study the problem of extending functions with values in a
locally convex Hausdorff space $E$ over a field $\mathbb{K}$, which have weak
extensions in a weighted Banach space $\mathcal{F}\nu(\Omega,\mathbb{K})$ of
scalar-valued functions on a set $\Omega$, to functions in a vector-valued
counterpart $\mathcal{F}\nu(\Omega,E)$ of $\mathcal{F}\nu(\Omega,\mathbb{K})$.
Our findings rely on a description of vector-valued functions as linear
continuous operators and extend results of Frerick, Jord\'{a} and Wengenroth.
As an application we derive weak-strong principles for continuously partially
differentiable functions of finite order, vector-valued versions of Blaschke's
convergence theorem for several spaces and Wolff type descriptions of dual
spaces.
