  The isomeric state of $^{16}$N was studied using the
$^{16}$N$^{g,m}$($d$,$^3$He)~proton-removal reactions at \mbox{11.8~MeV/$u$} in
inverse kinematics. The $^{16}$N beam, of which 24% was in the isomeric state,
was produced using the ATLAS in-fight facility and delivered to the HELIOS
spectrometer, which was used to analyze the $^{3}$He ions from the
($d$,$^{3}$He) reactions. The simultaneous measurement of reactions on both the
ground and isomeric states, reduced the systematic uncertainties from the
experiment and in the analysis. A direct and reliable comparison of the
relative spectroscopic factors was made based on a Distorted-Wave Born
Approximation approach. The experimental results suggest that the isomeric
state of $^{16}$N is an excited neutron-halo state. The results can be
understood through calculations using a Woods-Saxon potential model, which
captures the effects of weak-binding.
