Roughly how much would a teaspoon of neutron star material weigh?

Answer

Neutron stars pack more than the Sun's mass into a ball about 20 km wide. Exact figures depend on the star.

Context

A neutron star packs about 1.4 times the Sun's mass into a ball only around 20 kilometres across. The average density is roughly 10^14 times that of water, comparable to the density inside an atomic nucleus. A teaspoon is about 5 cubic centimetres, so at that density it would weigh on the order of a billion tonnes or more; quoted figures range from hundreds of millions to a few billion tons depending on the density and spoon size assumed, which is why the answer says 'billions of tons'.

Neutron stars form when the core of a massive star collapses in a supernova and gravity crushes protons and electrons together into neutrons. Pressure from the neutrons, a quantum effect, halts further collapse. The interior is not well known: layers are probably superfluid, the crust is a solid lattice, and the core could contain exotic particles that physicists are still trying to constrain with mass and radius measurements.

These objects are extreme in other ways. Pulsars are spinning neutron stars whose beams sweep past Earth like lighthouses; the Crab pulsar rotates about 30 times per second. Typical magnetic fields exceed a trillion gauss, and magnetars reach 10^14 to 10^15 gauss.

A teaspoon of the material could not exist alone: it is held together only by the star's immense gravity and would expand explosively if removed from it.