BiFeO$_3$ (BFO) shows both ferroelectricity and magnetic ordering at room temperature but its ferromagnetic component, which is due to spin canting, is negligible. Substitution of transition-metal atoms such as Co for Fe is known to enhance the ferromagnetic component in BFO. In order to reveal the origin of such magnetization enhancement, we performed soft x-ray absorption spectroscopy (XAS) and soft x-ray magnetic circular dichroism (XMCD) studies of BiFe$_{1-x}$Co$_x$O$_3$ ({it x} = 0 to 0.30) (BFCO) thin films grown on LaAlO$_3$(001) substrates. The XAS results indicated that the Fe and Co ions are in the Fe$^{3+}$ and Co$^{3+}$ states. The XMCD results showed that the Fe ions show ferromagnetism while the Co ions are antiferromagnetic at room temperature. The XAS and XMCD measurements also revealed that part of the Fe$^{3+}$ ions are tetrahedrally co-ordinated by oxygen ions but that the XMCD signals of the octahedrally coordinated Fe$^{3+}$ ions increase with Co content. The results suggest that an impurity phase such as the ferrimagnetic $gamma$-Fe$_2$O$_3$ which exists at low Co concentration decreases with increasing Co concentration and that the ferromagnetic component of the Fe$^{3+}$ ion in the octrahedral crystal fields increases with Co concentration, probably reflecting the increased canting of the Fe$^{3+}$ ions.