Carrier resupply while underway is primarily by a sort of temporary cable tramway erected between the carrier and the resupply ship.

Supercarriers came into existence at ~70,000t and transitioned to ~100,000t. You'd need to scale another step up or three, to 140,000t, 200,000t, or 280,000t, in order to see something capable of landing and taking off a cargo-laden C-130 in regular operations.