Polariton manipulations introduce novel approaches to modulate the near-field radiative heat transfer (NFRHT). Our theoretical investigation in this study centers on NFRHT in graphene-covered Weyl semimetals (WSMs). Our findings indicate variable heat flux enhancement or attenuation, contingent on chemical potential of graphene. Enhancement or attenuation mechanisms stem from the coupling or decoupling of surface plasmon polaritons (SPPs) in the graphene/WSM heterostructure. The graphene-covered WSM photon tunneling probabilities variation is demonstrated in detail. This research enhances our comprehension of SPPs within the graphene/WSM heterostructure and suggests methods for actively controlling NFRHT.