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