We define the notion of a weighted unfolding of quivers with real weights, and use this to provide a categorification of mutations of quivers of finite types
H
4
H_4
,
H
3
H_3
and
I
2
(
2
n
+
1
)
I_2(2n+1)
. In particular, the (un)folding induces a semiring action on the categories associated to the unfolded quivers of types
E
8
E_8
,
D
6
D_6
and
A
2
n
A_{2n}
respectively. We then define the tropical seed pattern on the folded quivers, which includes
c
c
- and
g
g
-vectors, and show its compatibility with the unfolding.