In nano-device applications using two-dimensional (2D) van der Waals materials, a heat dissipation through nano-scale interfaces can be a critical issue for optimizing device performances. By using a time-domain thermoreflectance measurement technique, we examine a cross-plane thermal transport through mono-layered (
n
= 1) and bi-layered (
n
= 2) WSe
2
flakes which are sandwiched by top metal layers of Al, Au, and Ti and the bottom Al
2
O
3
substrate. In these nanoscale structures with hetero- and homo-junctions, we observe that the thermal boundary resistance (TBR) is significantly enhanced as the number of WSe
2
layers increases. In particular, as the metal is changed from Al, to Au, and to Ti, we find an interesting trend of TBR depending on the WSe
2
thickness; when referenced to TBR for a system without WSe
2
, TBR for
n
= 1 decreases, but that for
n
= 2 increases. This result clearly demonstrates that the stronger bonding for Ti leads to a better thermal conduction between the metal and the WSe
2
layer, but in return gives rise to a large mismatch in the phonon density of states between the first and second WSe
2
layers so that the WSe
2
-WSe
2
interface becomes a major thermal resistance for
n
= 2. By using photoemission spectroscopy and optical second harmonic generation technique, we confirm that the metallization induces a change in the valence state of W-ions, and also recovers a non-centrosymmetry for the bi-layered WSe
2
.