How do ceramic disk insulators support the weight of transmission lines?
They sometimes do have a central core, but it's not metal.

For instance, Siemens make some silicone based insulators, and in their catalog they detail the core as:


  The core rod is boron-free, corrosion-resistant ECR2 glass-fiber-reinforced plastic rod (FRP rod). Due to the extremely high hydrolysis and acid resistance of the FRP rod the risk of so-called brittle fracture is completely eliminated on 3FL insulators.




Ceramic ones can be manufactured all in one piece as well where there is no internal support rod at all: