  We numerically study magnetic reconnection on different spatial scales and at
different heights in the weakly ionized plasma of the low solar atmosphere
(around $300-800$~km above the solar surface) within a reactive 2.5 D
multi-fluid plasma-neutral model. We consider a strongly magnetized plasma
($\beta \sim 6\% $) evolving from a force-free magnetic configuration and
perturbed to initialize formation of a reconnection current sheet. On large
scales, the resulting current sheets are observed to undergo a secondary
'plasmoid' instability. A series of simulations at different scales demonstrate
a cascading current sheet formation process that terminates for current sheets
with width of ~2m and length of $\sim100$~m, corresponding to the critical
current sheet aspect ratio of $\sim50$. We also observe that the plasmoid
instability is the primary physical mechanism accelerating the magnetic
reconnection in this plasma parameter regime. After plasmoid instabilities
appear, the reconnection rate sharply increases to a value of $\sim$ 0.035,
observed to be independent of the Lundquist number. These characteristics are
very similar to magnetic reconnection in fully ionized plasmas. In this low
$\beta$ guide field reconnection regime, both the recombination and
collisionless effects are observed to have a small contribution to the
reconnection rate. The simulations show that it is difficult to heat the dense
weakly ionized photospheric plasmas to above $2\times10^4$~K during the
magnetic reconnection process. However, the plasmas in the low solar
chromosphere can be heated above $3\times10^4$~K with reconnection magnetic
fields of $500$~G or stronger.
