Hi Gorblimey,
From my Point of view, If I was said Opponent, I would never have guessed the
hands you actually have (K4). I would have thought you do have pocket pair or AK/AQ/AJ. For the BB to protect his Hands like this, I can imagine him having either A2-A10, suited connectors, or pocket pairs as well.
If BB calls your half pot bet, he must see something he likes on the flop. Wouldn't call with suited connectors JT as an example. But A2, 56, 67? Probably would call.
On the other Hand, if you fire preflop and c-bet on flop, I would guess you must have now trips (AAA, 333, 555). With the Chance to a straight draw like here, I would call as the Opponent did. And on the turn - either you get lucky or the other gets lucky.
Bottomline, if you're Goal was to disguise your Hand and balance your Play - well done ;-)