How do we balance an FIR around its center?
How is a bit of an odd question. Trivially, we can make it balanced by making the taps symmetric. This can be done for both odd and even numbers of filter taps, by making it symmetric about the mid sampling time, or half-way between the two mid samples.

More to the point is why we should want to do this, and the effect it has on the response. A symmetric FIR filter has a linear phase response, that is, the same delay regardless of frequency. This is a very valuable property in many (but not all) filtering situations.