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 2.5D multifluid plasma-neutral model. We consider a strongly magnetized plasma (beta similar to 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 demonstrates a cascading current sheet formation process that terminates for current sheets with width of 2 m and length of similar to 100 m, corresponding to the critical current sheet aspect ratio of -50. 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 similar to 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 x 10(4) K during the magnetic reconnection process. However, the plasmas in the low solar chromosphere can be heated above 3 x 10(4) K with reconnection magnetic fields of 500 G or stronger.