  The structure and decay of the most neutron-rich beryllium isotope,
$^{16}$Be, has been investigated following proton knockout from a high-energy
$^{17}$B beam. Two relatively narrow resonances were observed for the first
time, with energies of $0.84(3)$ and $2.15(5)$ MeV above the two-neutron decay
threshold and widths of $0.32(8)$ and $0.95(15)$ MeV respectively. These were
assigned to be the ground ($J^{\pi}=0^+$) and first excited ($2^+$) state, with
$E_x=1.31(6)$ MeV. The mass excess of $^{16}$Be was thus deduced to be
$56.93(13)$ MeV, some $0.5$ MeV more bound than the only previous measurement.
Both states were observed to decay by direct two-neutron emission. Calculations
incorporating the evolution of the wavefunction during the decay as a genuine
three-body process reproduced the principal characteristics of the
neutron-neutron energy spectra for both levels, indicating that the ground
state exhibits a strong spatially compact dineutron component, while the 2$^+$
level presents a far more diffuse neutron-neutron distribution.
