Throw-weight is a term used to denote the carrying capacity of a ballistic missile. It is not quite the same as payload, which is usually taken to mean the weight of (or the capability to carry the weight of) any component, consumable or cargo of a launch vehicle which isn't required to make it function; the 'useful lift capacity.' This would include people, life support systems, spacecraft structure that wasn't part of the booster or required for the boost phase, and so on.

In the case of a ballistic missile, the throw-weight refers to the actual weight of the warheads delivered by the missile. This differs from the payload, since there are systems and structures in ballistic missiles (especially MIRVed ones) which don't have anything to do with launch or boost but aren't removable without compromising the mission, such as the warhead bus, guidance systems, etc. etc.

This term is limited to the ballistic missile context, be it ICBM, SLBM, IRBM, etc. It likely arises from the peculiarity of the ballistic missile in that it 'throws' its payload; unlike cruise missiles or aircraft which carry theirs, or spacecraft, which maneuver under their own power after leaving the booster. AFAIK, this is also restricted to suborbital boosts; using a ballistic missile to launch a satellite (which is more common these days, a happy change from Cold War days) would make the satellite a payload, since it's carried up into an orbit from whence it does not (immediately) re-enter and crash.