The recent experimental discovery of a Weyl semimetal in TaAs provides the first observation of a Weyl fermion in nature and demonstrates a novel type of anomalous surface state band structure, consisting of Fermi arcs. So far, work has focused on Weyl semimetals with strong spin-orbit coupling (SOC). However, Weyl semimetals with weak SOC may allow tunable spin-splitting for device applications and may exhibit a crossover to a spinless topological phase, such as a Dirac line semimetal in the case of spinless TaAs. NbP, isostructural to TaAs, may realize the first Weyl semimetal in the limit of weak SOC. Here we study the surface states of NbP by angle-resolved photoemission spectroscopy (ARPES) and we find that we $\textit{cannot}$ show Fermi arcs based on our experimental data alone. We present an $\textit{ab initio}$ calculation of the surface states of NbP and we find that the Weyl points are too close and the Fermi level is too low to show Fermi arcs either by (1) directly measuring an arc or (2) counting chiralities of edge modes on a closed path. Nonetheless, the excellent agreement between our experimental data and numerical calculations suggests that NbP is a Weyl semimetal, consistent with TaAs, and that we observe trivial surface states which evolve continuously from the topological Fermi arcs above the Fermi level. Based on these results, we propose a slightly different criterion for a Fermi arc which, unlike (1) and (2) above, does not require us to resolve Weyl points or the spin splitting of surface states. We propose that raising the Fermi level by $> 20$ meV would make it possible to observe a Fermi arc using this criterion in NbP. Our work offers insight into Weyl semimetals with weak spin-orbit coupling, as well as the crossover from the spinful topological Weyl semimetal to the spinless topological Dirac line semimetal. ; Comment: This work was based on the theoretical prediction of a Weyl semimetal in the TaAs family of compounds, http://www.nature.com/ncomms/2015/150612/ncomms8373/full/ncomms8373.html