  In big bang nucleosynthesis (BBN), the light matter abundance is dictated by
the neutron-to-proton ($n/p$) ratio which is controlled by the standard weak
processes in the early universe. Here, we study the effect of an extra particle
species ($\chi$) which \textit{co-annihilates} with neutron (proton), thereby
potentially changing the ($n/p$) ratio in addition to the former processes. We
find a novel interplay between the co-annihilation and the weak interaction in
deciding the ($n/p$) ratio and the yield of $\chi$. Large co-annihilation
strength ($G_D$) in comparison to the weak coupling ($G_F$), potentially can
alter the number of nucleons in the thermal bath modifying the ($n/p$) ratio
from its standard evolution. We find that the standard BBN prediction is
restored for $G_D/G_F \lesssim 10^{-2}$, while the mass of $\chi$ being much
smaller than the neutron mass. When the mass of $\chi$ is comparable to the
neutron mass, we can allow large $G_D/G_F ~(\gtrsim 10^2)$ values, as the
thermal abundance of $\chi$ becomes Boltzmann-suppressed. Therefore, the
($n/p$) ratio is restored to its standard value via dominant weak processes in
later epochs. We also discuss the stability of the new particle in an effective
theroy framework for co-annihilation. Further, the co-annihilation interaction
generates elastic scattering of $\chi$ and nucleons at the next-to-leading
order. This provides a way to probe the scenario in direct detection
experiments, if $\chi$ is accidentally stable over cosmological timescale.
