Parabolic sheaves with real weights as sheaves on the Kato-Nakayama space

We define quasi-coherent parabolic sheaves with real weights on a fine saturated log analytic space, and explain how to interpret them as quasi-coherent sheaves of modules on its Kato-Nakayama space. This recovers the description as sheaves on root stacks of [5] and [27] for rational weights, but also includes the case of arbitrary real weights.