I am a bit confused as to how having a one-card bdfd along with SDV (weak top pair, for instance) should influence our decision to cbet or not. The advantages of betting with each seem to be:

When we do not have the bdfd: there are more hands we can get value/protection from by betting.

When we do have the bdfd: we have slightly better equity vs. our opponent's continuing range and potentially turning our hand into a bluff on a later street becomes more of an option.

So for example, let's say we open CO with Q8o (for whatever reason) and the BB who is a reg calls. Flop is Qs7s4d. If we have the 8 of spades in our hand, should we be more or less likely to cbet?