  Using high-resolution photoemission spectroscopy and first-principles
calculations, we characterize superconducting TlNi$_2$Se$_2$ as a material with
weak electronic Coulomb correlations leading to a bandwidth renormalization of
1.4. We identify a camelback-shaped band, whose energetic position strongly
depends on the selenium height. While this feature is universal in transition
metal pnictides, in TlNi$_2$Se$_2$ it lies in the immediate vicinity of the
Fermi level, giving rise to a pronounced van Hove singularity. The resulting
heavy band mass resolves the apparent puzzle of a large normal-state specific
heat coefficient (Phys. Rev. Lett. 112, 207001) in this weakly correlated
compound.
