Brute-forcing Symmetric Keys Random keys are often produced using high-quality random generators. Assuming a key produced for a symmetrical cipher, this means that the number of zeros and ones in the key will, on average, concentrate on about half of the key's length.

Having this in mind, is it anywhere more profitable to start a brute-force attack from bit patterns with similar population counts (that is, with similar counts of ones and zeros)? Will this increase the probability of success?
No, it doesn't help.  It doesn't hurt either; as long as you don't repeat keys, the probability of success is always the same.  That is, if there are $2^n$ possible keys, and you test $\lambda$ of them, the probability you hit the right one is always $\lambda / 2^{n}$.

A key generated by a high quality random number generator (or a good key derivation function) is equidistributed; every possible value has an equal probability of being the correct one.  Yes, most keys will have approximately the same number of 0's and 1's; but that's because most possible values will have approximately the same number of 0's and 1's.